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Journal of Soviet Mathematics

, Volume 1, Issue 5, pp 594–620 | Cite as

Arithmetic on algebraic varieties

  • A. N. Parshin
Article

Keywords

Algebraic Variety 
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Literature cited

  1. 1.
    A. N. Andrianov, “Representation of numbers by certain quadratic forms in connection with the theory of elliptic curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 29(1):227–238 (1965).Google Scholar
  2. 2.
    A. N. Andrianov, “Zeta-functions of simple algebras with non-Abelian characters,” Uspekhi Mat. Nauk, 23(4):3–66 (1968).Google Scholar
  3. 3.
    M. I. Bashmakov, “On the divisibility of homogeneous principal bundles over Abelian varieties,” Izv. Akad. Nauk SSSR, Ser. Mat., 28(3):661–664 (1964).Google Scholar
  4. 4.
    M. I. Bashmakov, “On the rank of Abelian varieties,” Dokl. Akad. Nauk SSSR, 181(5):1031–1033 (1968).Google Scholar
  5. 5.
    M.I. Bashmakov, “On the Shafarevich-Tate group of an elliptic curve,” Mat. Zametki, 7(1):79–86 (1970).Google Scholar
  6. 6.
    Z.I. Borevich and I. R. Shafarevich, Theory of Numbers [in Russian], “Nauka,” Moscow (1964).Google Scholar
  7. 7.
    A. Borel, “Hecke operators and zeta-functions,” Matematika (Periodical collection of translations of foreign articles), 13(4):45–60 (1969).Google Scholar
  8. 8.
    K. B. Bulataev, “On one rational method of computing rational ideals of degree zero on a curve of genus 2,ay2=5(x2+3x+1)(−1+6x2−x4),” Tr. Kirg. Univ.,Ser. Mat. Nauk, No. 6, 23–25 (1967).Google Scholar
  9. 9.
    K. B. Bulataev, “Estimate of the rank of a hyperelliptic curve of genus 2,” Sb. Statei Aspirantov Kirg. Univ., Fiz.-Mat. i Estestv. Nauk, No. 2, 6–14 (1968).Google Scholar
  10. 10.
    K. B. Bulataev, “Estimate of the rank of the curves y2=(−l/3)(x2+x+l)(3x3+4x2+3x), y2=(x2+3x+1) (−1+6x2−x4),” Sb. Statei Aspirantov Kirg. Univ., Fiz.-Mat. i Estestv. Nauk, No. 3, 3–8 (1969).Google Scholar
  11. 11.
    Yu. R. Bainberg, “On the reduction of formal groups modulo a prime,” Sibirsk. Mat. Zh., 4(6):1263–1270 (1963).Google Scholar
  12. 12.
    Yu. R. Bainberg, “Algebraic varieties over fields with differentiation,” Mat. Sb., 80(3):417–444 (1969).Google Scholar
  13. 13.
    O. M. Vvedenskii (O. N. Vvedenskii), “Cohomology of Lutz subgroups of an elliptic curve,” Zb. Robit. Aspirantiv L'vivsk. Univ., Prirodn. Nauk., L'viv (1963), pp. 5–8.Google Scholar
  14. 14.
    O. M. Vvedenskii (O. N. Vvedenskii), “Duality in elliptic curves over a local field. I,” Izv. Akad. Nauk SSSR, Ser. Mat., 28(5):1091–1112 (1964).Google Scholar
  15. 15.
    O. M. Vvedenskii (O. N. Vvedenskii), “Torsion of elliptic curves over a local field,” Visnik L'viv. Univ., Ser. Mekh.-Mat., No. 1, 3–6 (1965).Google Scholar
  16. 16.
    O. M. Vvedenskii (O. N. Vvedenskii), “Elliptic curves with a degenerate reduction,” Vestnik L'vov. Polytekhn. Inst., No. 8, 70–72 (1965).Google Scholar
  17. 17.
    O. M. Vvedenskii (O. N. Vvedenskii), “Proalgebraic groups with reduction height two,” Visnik L'viv. Derzh. Univ., Ser. Mekh.-Mat., No. 2, 24–29 (1965).Google Scholar
  18. 18.
    O. M. Vvedenskii (O. N. Vvedenskii), “Duality in elliptic curves over a local field. II,” Izv. Akad. Nauk SSSR, Ser. Mat., 30(4):891–922 (1966).Google Scholar
  19. 19.
    O. M. Vvedenskii (O. N. Vvedenskii), “Local class fields of elliptic curves,” Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, No. 10, 876–880 (1968).Google Scholar
  20. 20.
    O. M. Vvedenskii (O. N. Vvedenskii), “‘Local class fields’ of elliptic curves,” Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, No. 5, 393–396 (1969).Google Scholar
  21. 21.
    O. M. Vvedenskii (O. N. Vvedenskii), “‘Local class fields’ of elliptic curves,” Dopovidi Akad. Ukrain. RSR, Ser. A, No. 11, 966–969 (1969).Google Scholar
  22. 22.
    A. Weil, Adeles and Algebraic Groups, Inst. Adv. Studies, Princeton, N. J. (1961).Google Scholar
  23. 23.
    V. E. Voskresenskii, “On the decomposition of genus into classes in uniform spaces,” Volzhsk. Mat. Sb., No. 2, 21–25 (1964).Google Scholar
  24. 24.
    V. E. Voskresenskii, “On two-dimensional algebraic tori,” Izv. Akad. Nauk SSSR, Ser. Mat., 29(1):239–244 (1965).Google Scholar
  25. 25.
    V. E. Voskresenskii, “On two-dimensional algebraic tori. II,” Izv. Akad. Nauk SSSR, Ser. Mat., 31(3):711–716 (1967).Google Scholar
  26. 26.
    V. E. Voskresenskii, “Arithmetic on ∑-varieties,” in: Research on Number Theory, No. 2 [in Russian], Saratov Univ., Saratov (1968), pp. 50–59.Google Scholar
  27. 27.
    V. E. Voskresenskii, “Picard groups of linear algebraic groups,” in: Research on Number Theory, No. 3 [in Russian], Saratov Univ., Saratov (1969), pp. 7–16.Google Scholar
  28. 28.
    V. E. Voskresenskii, “On the birational equivalence of linear algebraic groups,” Dokl. Akad. Nauk SSSR, 188(5):978–981 (1969).Google Scholar
  29. 29.
    V. E. Voskresenskii, “The birational properties of linear algebraic groups,” Izv. Akad. Nauk SSSR, Ser. Mat., 34(1):3–19 (1970).Google Scholar
  30. 30.
    A. O. Gel'fond and Yu. V. Linnik, Elementary Methods in Analytic Number Theory [in Russian], Fizmatgiz, Moscow (1962), 272 pp.Google Scholar
  31. 31.
    S. G. Gindkikin and I. I. Pyatetskii-Shapiro, “On the algebraic structure of the field of Siegel's modular functions,” Dokl. Akad. Nauk SSSR, 162(6):1226–1229 (1965).Google Scholar
  32. 32.
    V. A. Dem'yanenko, “Rational points of one class of algebraic curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 30(6):1373–1396 (1966).Google Scholar
  33. 33.
    V. A. Dem'yanenko, “Rational points of one class of algebraic curves,” Dokl. Akad. Nauk SSSR, Ser. Mat., 171(6):1259–1266 (1966).Google Scholar
  34. 34.
    V. A. Dem'yanenko, “On points of finite order on elliptic curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 31(6):1327–1340 (1967).Google Scholar
  35. 35.
    V. A. Dem'yanenko, “On the rational points of certain curves of higher genus,” Acta Arith., 12(4):333–354 (1967).Google Scholar
  36. 36.
    V. A. Dem'yanenko, “Estimate of the remainder term in Tate's formula,” Mat. Zametki, 3(3):271–278 (1968).Google Scholar
  37. 37.
    V. A. Dem'yanenko, “On the indeterminate equations x6+y6=az2, x6+y4=az3, x4+y4=az4,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 4, 26–32 (1968).Google Scholar
  38. 38.
    V. A. Dem'yanenko, “On points of finite order of elliptic curves,” Mat. Zametki, 7(5):563–567 (1970).Google Scholar
  39. 39.
    I. V. Elistratov, “On the number of solutions of certain equations in finite fields,” Tr. Molodykh Uchebykh. Saratovsk. Univ., Vyp. Mat., Saratov (1964), pp. 27–30.Google Scholar
  40. 40.
    I. V. Elistratov, “On the number of solutions of certain equations in finite fields,” in: Certain Aspects of Field Theory [in Russian], Saratov Univ., Saratov (1964), pp. 48–59.Google Scholar
  41. 41.
    I. V. Elistratov, “On an elementary proof of Hasse's theorem,” in: Research on Number Theory, No. 1 [in Russian], Saratov Univ., Saratov (1966), pp. 21–26.Google Scholar
  42. 42.
    I. V. Elistratov, “Number of classes and location of zeros of the Z(u)-function,” Volzhsk. Mat. Sb., No. 4, 58–65 (1966).Google Scholar
  43. 43.
    Yu. L. Érshov, “Undecidability of certain fields,” Dokl. Akad. Nauk SSSR, 161(1):27–29 (1965).Google Scholar
  44. 44.
    Yu. L. Érshov, “On elementary theories of local fields,” Algebra i Logika, Seminar, 4(2):5–30 (1965).Google Scholar
  45. 45.
    Yu. L. Érshov, “On the rational points over Henselian fields,” Algebra i Logika, Seminar, 6(3):39–49 (1967).Google Scholar
  46. 46.
    K. Iwasawa, “Analogy between the fields of algebraic numbers and of algebraic functions,” Sugaku, 15(2):65–67 (1963).Google Scholar
  47. 47.
    V. A. Iskovskikh, “On birational forms of rational surfaces,” Izv. Akad. Nauk SSSR, Ser. Mat., 29(6):1417–1433 (1965).Google Scholar
  48. 48.
    V. A. Iskovskikh, “Rational surfaces with a pencil of rational curves,” Mat. Sb., 74(4):608–638 (1967).Google Scholar
  49. 49.
    Y. Ihara, “Algebraic curves mod p and arithmetic groups,” Matematika (Periodical collection of translations of foreign articles), 12(6):56–62 (1968).Google Scholar
  50. 50.
    K. Karabaev, “On one rational method for seeking certain rational divisors of zero degree on the curveay2=(x2+l)(x3+x2+x) of genus 2,” Sb. Statei Aspirantov Kirg. Univ., Fiz.-Mat. i Estestv. Nauk, No. 2, 23–28 (1968).Google Scholar
  51. 51.
    N. Katz and T. Oda, “On the differentiation with respect to a parameter of de Rham cohomology classes,” Matematika (Periodical collection of translations of foreign articles), 14(2):91–101 (1970).Google Scholar
  52. 52.
    B. Kh. Kirshtein and I. I. Pyatetskii-Shapiro, “Invariant subrings of induced rings,” Izv. Akad. Nauk SSSR, Ser. Mat., 34(1):83–89 (1970).Google Scholar
  53. 53.
    A.I. Lapin, “On subfields of hyperelliptic fields. I,” Izv. Akad. Nauk SSSR, Ser. Mat., 28(5):953–988 (1964).Google Scholar
  54. 54.
    A. I. Lapin, “On the rational points of an elliptic curve,” Izv. Akad. Nauk SSSR, Ser. Mat., 29(3):701–716 (1965).Google Scholar
  55. 55.
    Yu. I. Manin, “Diophantine equations and algebraic geometry,” Proc. Fourth All-Union Math. Congress, Vol. 2, 1961 [in Russian], “Nauka,” Leningrad (1964), pp. 15–21.Google Scholar
  56. 56.
    Yu. I. Manin, “Formal and algebraic commutative groups,” Uspekhi Mat. Nauk, 17(2):197–198 (1962).Google Scholar
  57. 57.
    Yu. I. Manin, “Two-dimensional formal Abelian groups,” Dokl. Akad. Nauk SSSR, 143(1):35–37 (1962).Google Scholar
  58. 58.
    Yu. I. Manin, “On the classification of formal Abelian groups,” Dokl. Akad. Nauk SSSR, 144(3):490–492 (1962).Google Scholar
  59. 59.
    Yu. I. Manin, “Proof of an analog of Mordell's conjecture for algebraic curves over functional fields,” Dokl. Akad. Nauk SSSR, 152(5):1061–1063 (1963).Google Scholar
  60. 60.
    Yu. I. Manin, “Rational points of algebraic curves over functional fields,” Izv. Akad. Nauk SSSR, Ser. Mat., 27(6):1395–1440 (1963).Google Scholar
  61. 61.
    Yu. I. Manin, “On arithemetic on rational surfaces,” Dokl. Akad. Nauk SSSR, 152(1):46–49 (1963).Google Scholar
  62. 62.
    Yu. I. Manin, “Theory of commutative formal groups over fields of finite characteristic,” Uspekhi Mat. Nauk, 18(6):3–90 (1963).Google Scholar
  63. 63.
    Yu. I. Manin, “Rational points on algebraic curves,” Uspekhi Mat. Nauk, 19(6):83–87 (1964).Google Scholar
  64. 64.
    Yu. I. Manin, “The Tate height of points on an Abelian variety, its variants and applications,” Izv. Akad. Nauk SSSR, Ser. Mat., 28(6):1363–1390 (1964).Google Scholar
  65. 65.
    Yu. I. Manin, “Differential forms and sections of elliptic pencils,” in: Modern Problems in Analytic Function Theory [in Russian], “Nauka,” Moscow (1966), pp. 224–229.Google Scholar
  66. 66.
    Yu. I. Manin, “Rational surfaces over perfect fields. I,” Publs. Math. Inst. Hautes Études Scient., No. 30, 55–113 (1966).Google Scholar
  67. 67.
    Yu. I. Manin, “Rational G-surfaces,” Dokl. Akad. Nauk SSSR, 175(1):28–30 (1967).Google Scholar
  68. 68.
    Yu. I. Manin, “Rational surfaces over perfect fields. II,” Mat. Sb., 72(2):161–192 (1967).Google Scholar
  69. 69.
    Yu. I. Manin, “Rational surfaces and Galois cohomology,” Proc. Internat. Congr. Mathematicians, 1966 [in Russian], “Mir,” Moscow (1968), pp. 495–509.Google Scholar
  70. 70.
    Yu. I. Manin, “Cubic hypersurfaces. I. Quasigroups of classes of points,” Izv. Akad. Nauk SSSR, Ser. Mat., 32(6):1223–1244 (1968).Google Scholar
  71. 71.
    Yu. I. Manin, “On certain groups connected with cubic varieties,” Uspekhi Mat. Nauk, 23(1):212 (1968).Google Scholar
  72. 72.
    Yu. I. Manin, “Correspondences, motifs, and monoidal transformations,” Mat. Sb., 77(4):475–507 (1968).Google Scholar
  73. 73.
    Yu. I. Manin, “The p-torsion of elliptic curves is uniformly bounded,” Izv. Akad. Nauk SSSR, Ser. Mat., 33(3):459–465 (1969).Google Scholar
  74. 74.
    Yu. I. Manin, “On Hilbert's twelfth problem,” in: The Hilbert Problems [in Russian], “Nauka,” Moscow (1969), pp. 159–162.Google Scholar
  75. 75.
    Yu. I. Manin, “Cubic hypersurfaces. III. Moufang loops and Brauer equivalences,” Mat. Sb., 79(2):155–170 (1969).Google Scholar
  76. 76.
    G. N. Markshaitis, “On p-extensions with one critical number,” Izv. Akad. Nauk SSSR, Ser. Mat., 27(2):463–466 (1963).Google Scholar
  77. 77.
    G. N. Markshaitis, “On certain elliptic curves,” Lit. Mat. Sb., 9(2):402–403 (1969).Google Scholar
  78. 78.
    Yu. V. Matiyasevich, “Diophantineness of denumberable sets,” Dokl. Akad. Nauk SSSR, 191(2):279–282 (1970).Google Scholar
  79. 79.
    P. A. Medvedev, “On the representation of zero by a cubic form in the field of p-adic number,” Uspekhi Mat. Nauk, 19(6):187–190 (1964).Google Scholar
  80. 80.
    P. A. Medvedev, “Orders and indices of an elliptic curve,” Izv. Akad. Nauk SSSR, Ser. Mat., 30(5):1179–1192 (1966).Google Scholar
  81. 81.
    P. A. Medvedev, “A remark on my paper ‘Orders and indices of an elliptic curve,’” Izv. Akad. Nauk SSSR, Ser. Mat., 32(1):247 (1968).Google Scholar
  82. 82.
    M. E. Novodvorskii and I. I. Pyatetskii-Shapiro, “Some remarks on the torsion of elliptic curves,” Mat. Sb., 82(2):309–316 (1970).Google Scholar
  83. 83.
    S. V. Ogai, “On rational points on the curve y2=x(x2+ax+b),” Tr. Mat. Inst. Akad. Nauk SSSR, 80:110–116 (1965).Google Scholar
  84. 84.
    S. V. Ogai, “On the maps of the curvesay2=(z2−2)(z−2),ay2=(z2−z)(z+2) into the curveay2=x5+x,” Tr. Kirg. Univ., Ser. Mat. Nauk, No. 6, 45–49 (1967).Google Scholar
  85. 85.
    S. V. Ogai, “Estimate of the rank of certain hyperelliptic curves of genus 2,” Tr. Kirg. Univ., Ser. Mat. Nauk, No. 5, 144–148 (1968).Google Scholar
  86. 86.
    A. N. Parshin, “Algebraic curves over functional fields,” Dokl. Akad. Nauk SSSR, 183(3):524–526 (1968).Google Scholar
  87. 87.
    A. N. Parshin, “Algebraic curves over functional fields. I,” Izv. Akad. Nauk SSSR, Ser. Mat., 32(5):1191–1219 (1968).Google Scholar
  88. 88.
    A. N. Parshin, “Isogenies and torsion of elliptic curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 34(2):409–424 (1970).Google Scholar
  89. 89.
    G. I. Perel'muter, “On certain sums and on the varieties connected with them,” Tr. Molodykh Uchenykh. Satatovsk. Univ., Vyp. Mat., Saratov (1964), pp. 27–30.Google Scholar
  90. 90.
    G. I. Perel'muter, “Z-functions of one class of cubic surfaces,” in: Research on Number Theory, No. 1 [in Russian], Saratov Univ., Saratov (1966), pp. 49–58.Google Scholar
  91. 91.
    G. I. Perel'muter, “Rationality of L-functions of one class of algebraic varieties,” in: Research on Number Theory, No. 1 [in Russian], Saratov Univ., Saratov (1966), pp. 59–62.Google Scholar
  92. 92.
    G. I. Perel'muter, “Estimate of a sum along an algebraic curve,” Mat. Zametki, 5(3):373–380 (1969).Google Scholar
  93. 93.
    I. I. Pyatetskii-Shapiro, “On the reduction modulo a prime of the field of modular functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 32(6):1264–1274 (1968).Google Scholar
  94. 94.
    I. I. Pyatetskii-Shapiro, “Induced rings and the reduction of the field of automorphic functions,” Funkts. Analiz i Ego Prilozhen., 4(1):94 (1970).Google Scholar
  95. 95.
    I. I. Pyatetskii-Shapiro and I. R. Shafarevich, “Galois theory of transcendental extensions and uniformizations,” Izv. Akad. Nauk SSSR, Ser. Mat., 30(3):671–704 (1966).Google Scholar
  96. 96.
    I. I. Pyatetskii-Shapiro and I. R. Shafarevich, “Galois theory of transcendental extensions and uniformizations,” in: Modern Problems in Analytic Function Theory [in Russian], “Nauka,” Moscow (1966), pp. 262–264.Google Scholar
  97. 97.
    M. Sanuke, “Rational points of algebraic curves over functional fields,” Sugaku, 20(1):23–25 (1968).Google Scholar
  98. 98.
    Seminar on Complex Multiplication, 1–6. Matematika (Periodical collection of translations of foreign articles), 12(1):55–95 (1968).Google Scholar
  99. 99.
    S. A. Stepanov, “On the number of points of a hyperelliptic curve over a simple finite field,” Izv. Akad. Nauk SSSR, Ser. Mat., 33(5):1171–1181 (1969).Google Scholar
  100. 100.
    J. T. Tate and I. R. Shafarevich, “On the rank of elliptic curves,” Dokl. Akad. Nauk SSSR, 175(4):770–773 (1967).Google Scholar
  101. 101.
    T. A. Tushkina, “Numerical experiment on the computation of the Hasse invariant for certain curves,” Izv. Akad. Nauk SSSR, Ser. Mat., 29(5):1203–1204 (1965).Google Scholar
  102. 102.
    D. K. Faddeev, “On a paper by A. Baker,” Zap. Nauchn. Seminarov Leningrad. Otdel. Mat. Inst. Akad. Nauk SSSR, 1:128–139 (1966).Google Scholar
  103. 103.
    Yu. I. Khmelevskii, “On Hilbert's tenth problem,” in: The Hilbert Problems [in Russian], “Nauka,” Moscow, 141–153.Google Scholar
  104. 104.
    I. R. Shafarevich, “On the birational equivalence of elliptic curves,” Dokl. Akad. Nauk SSSR, 114(2):267–270 (1957).Google Scholar
  105. 105.
    I. R. Shafarevich, “Indices of elliptic curves,” Dokl. Akad. Nauk SSSR, 114(4):714–716 (1957).Google Scholar
  106. 106.
    I. R. Shafarevich, “The group of principal uniform algebraic varieties,” Dokl. Akad. Nauk SSSR, 124(1):42–43 (1959).Google Scholar
  107. 107.
    I. R. Shafarevich, “Principal uniform spaces defined over a function field,” Tr. Mat. Inst. Akad. Nauk SSSR, 64:316–346 (1961).Google Scholar
  108. 108.
    I. R. Shafarevich, “Algebraic number fields,” Proc. Internat. Congr. Math., Aug. 1962, Djursholm. Uppsala, Sweden (1963), pp. 163–176.Google Scholar
  109. 109.
    I. R. Shafarevich, “Abelian varieties over algebraic number fields,” Proc. Fourth All-Union Math. Congr., 1961, Vol. 2 [in Russian], “Nauka,” Leningrad (1964), p. 47.Google Scholar
  110. 110.
    I. R. Shafarevich, Zeta-Functions. 1966–1967 [in Russian], (Mosk. Univ. Makh.-Mat. Fak., Mosk. Mat. Obshch.), Moscow (1969), p. 148.Google Scholar
  111. 111.
    Algebraic Geometry. Pap. Bombay Colloq., 1968. London, Oxford Univ. Press, 1969, viii, 426pp., ill.Google Scholar
  112. 112.
    Algebraic number theory. London, 1967.Google Scholar
  113. 113.
    A. Altman, “Transcendental and algebraic points on group varieties,” Doct. diss. Columbia Univ., 1968, 45 pp. Dissert. Abstrs., B29(6):2107 (1968).Google Scholar
  114. 114.
    K. Amano, “A note on Galois cohomology groups of algebraic tori,” Nagoya Math. J., 34:121–127 (1969).Google Scholar
  115. 115.
    Arbeitsgemeinschaft Prof. Dr. P. Roquett, “Schmale W. (Tagungsbericht 18 und 19 Mai 1968, No. 13) Math. Forschungsinst,” Oberwohlfach, 6S (1968).Google Scholar
  116. 116.
    G. Archinard, “Théorie de Chabauty sur les équations diophantiennes I.,” Sémin. Théor. normbres Delange-Pisot. Fac. sci. Paris, 7(16):1–23 fasc. 2, 1965–1966 (1967).Google Scholar
  117. 117.
    G. Archinard, “Théorie de Chabauty sur les équations diophantiennes. II,” Semin. Delange-Pisot-Poitou. Fac. Sci. Paris, 8(1):5/01–5/13 1966–1967 (1968).Google Scholar
  118. 118.
    C. Arf, “Sur la structure du groupe de Galois de la fermetrure algébrique d'un corps de séries de puissances sur un corps fini et les conducteurs d'Artin,” Colloq. internat. Centre nat. rech. scient., 143:27–35 (1966).Google Scholar
  119. 119.
    Arithmetical algebraic geometry, “Proc. Conf., Purdue Univ., Dec. 5–7 1963. Ed. Schilling O. F. G., New York, Harper and Row, 1965, VIII, p. 200.Google Scholar
  120. 120.
    J. V. Armitage, “Algebraic functions and an analogue of the geometry of numbers: the Riemann-Roch thoerem,” Arch. Math., 18(4):383–393 (1967).Google Scholar
  121. 121.
    J. V. Armitage, “The Thue-Siegel-Roth theorem in characteristic p,” J. Algebra, 9(2):183–189 (1968).Google Scholar
  122. 122.
    E. Artin, “Algebraic numbers and algebraic functions,” London, Nelson, 1968, XIII, p. 349, Brit. Nat. Bibliogr., 14(968) (1968).Google Scholar
  123. 123.
    M. Artin, “On the solutions of analytic equations,” Invent, math., 5(4):277–291 (1968).Google Scholar
  124. 124.
    M. Artin, “Algebraic approximation of structures over complete local rings,” Publs math. Inst. hautes études scient, 36:23–58 (1969).Google Scholar
  125. 125.
    A. O. L. Arkin, “Note on a paper of Birch,” J. London Math. Soc., 44(2):283 (1968).Google Scholar
  126. 126.
    B. Auslander, “The Brauer group of a ringed space,” J. Algebra, 4(2):220–273 (1966).Google Scholar
  127. 127.
    M. Auslander and A. Brummer, “Brauer groups of discrete valuation rings,” Proc. Koninkl. nederl. akad. wet, A71(3):286–296 (1968). Indagationes math., 30(3):286–296 (1968).Google Scholar
  128. 128.
    J. Ax, “Zeroes of polynomials over finite fields,” Amer. J. Math., 86(2):255–261 (1964).Google Scholar
  129. 129.
    J. Ax, “A field of cohomological dimension 1 which is not C1,” Bull. Amer. Math. Soc., 71(5):717 (1965).Google Scholar
  130. 130.
    J. Ax, “Proof of some conjectures on cohomological dimension,” Proc. Amer. Math. Soc., 16(6):1214–1221 (1965).Google Scholar
  131. 131.
    J. Ax, “Solving Diophantine problems modulo every prime,” Ann. Math., 85(2):161–183 (1967).Google Scholar
  132. 132.
    J. Ax, “The elementary theory of finite fields,” Ann. Math., 88(2):239–271 (1968).Google Scholar
  133. 133.
    J. Ax and S. Kochen, “Diophantine problems over local fields. I,” Amer. J. Math., 87(3):605–630 (1965).Google Scholar
  134. 134.
    J. Ax and S. Kochen, “Diophantine problems over local fields. II,” A complete set of axioms for p-adic number theory. Amer. J. Math., 87(3):631–648 (1965).Google Scholar
  135. 135.
    W. L. Baily, Jr., “On the moduli of Abelian varieties with multiplications from an order in a totally real number field,” Proc. Internat. Congr. Math. Aug. 1962, Djursholm. Uppsala, 309–313 (1963).Google Scholar
  136. 136.
    W. L. Baily, Jr., “On the moduli of Abelian varieties with multiplications,” J. Math. Soc. Japan, 15(4):367–386 (1963).Google Scholar
  137. 137.
    A. Baker, “Contributions to the theory of Diophantine equations. I,” On the representation of integers by binary forms. Philos. Trans. Roy. Soc. London, A263(1139):173–191 (1968).Google Scholar
  138. 138.
    A. Baker, “Conributions to the theory of Diophantine equations. II,” The Diophantine equation y2=x3+k. Philos. Trans. Roy. Soc. London, A263(1139):193–208 (1968).Google Scholar
  139. 139.
    A. Baker, “Bounds for the solutions of the hyperelliptic equation,” Proc. Cambridge Philos. Soc., 65(2):439–444 (1969).Google Scholar
  140. 140.
    A. Baker and J. Coates, “Integer points on curves of genus 1,” Proc. Cambridge Phil. Soc., 67(3):595–602 (1970).Google Scholar
  141. 141.
    J. Barshay, “On the zeta-function of certain algebraic varieties,” Doct. diss. Brandeis Univ., 1966, p. 82, Dissert. Abstrs, B27(10):3585–3586 (1967).Google Scholar
  142. 142.
    J. Barshay, “On the zeta-function of biprojective complete intersections,” Trans. Amer. Math. Soc., 135:447–458 Jan, (1969).Google Scholar
  143. 143.
    I. Barsotti, “Analytical methods for abelian varieties in positive characteristic,” Colloq. théor. groupes algébr. Bruxelles, 1962. Louvain-Paris, 77–85 (1962).Google Scholar
  144. 144.
    I. Barsotti, “Metodi analitici per varietá abeliane in caratteristica positiva,” Capitoli 3, 4. Ann. Scuola norm. super. Pisa. Sci fis. e mat., 19(2):277–330 (1965).Google Scholar
  145. 145.
    I. Barsotti, “Metodi analitici per varietá abeliane in caratteristica positiva,” Capitolo 5. Ann. Scuola norm, super. Pisa Sci. fis e mat., 19(4):481–512 (1965).Google Scholar
  146. 146.
    I. Barsotti, “Metodi analitici per varietá abeliane in caratteristica positiva,” Capitolo 6. Ann. Scuola norm, super. Pisa Sci. fis. e mat., 20(1):101–137 (1966).Google Scholar
  147. 147.
    I. Barsotti, “Metodi analitici per varietá abeliane in caratteristica positiva,” Capitolo 7. Ann. Scuola norm. super. Pisa Sci. fis. e mat., 20(2):331–365 (1966).Google Scholar
  148. 148.
    I. Barsotti, “Svilappi e applicazioni della teoria dei gruppi analitici,” Boll. Uni-one mat. ital., 1(2):187–206 (1968).Google Scholar
  149. 149.
    I. Barsotti, “Varietá abeliane su corpi p-adici,” Part 1. Sympos. math. 1967–1968, Vol. 1. Gubbio, 109–173 (1969).Google Scholar
  150. 150.
    W. Bartenwerfer, “Einige Fortsetzungssatze in der p-adischen Analysis,” Math. Ann., 185(3):191–210 (1970).Google Scholar
  151. 151.
    A. Bialynicki-Birula, “Remarks on relatively minimal models of fields of genus 0. I,” Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 15(5):301–304 (1967).Google Scholar
  152. 152.
    A. Bialynicki-Birula, “Remarks on relatively minimal models of fields of genus 0. II,” Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 16(2):81–85 (1968).Google Scholar
  153. 153.
    A. Bialynicki-Birula, “Remarks on relatively minimal models of fields of genus 0. III,” Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 17(7)419–424 (1969).Google Scholar
  154. 154.
    A. Bialynicki-Birula, “A note on deformations of Severi-Brauer varieties and relatively minimal models of fields of genus 0,” Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 18(4):175–176 (1970).Google Scholar
  155. 155.
    B. J. Birch, “Conjectures concerning elliptic curves,” Theory numbers. Providence, R. I., Amer. Soc., 106–112 (1965).Google Scholar
  156. 156.
    B. J. Birch, “Rational points of elliptic curves,” in: Internat. Congr. Mathematicians. Report Abstracts [in Russian], Moscow (1966), pp. 37–38.Google Scholar
  157. 157.
    B. J. Birch, “How the number of points of an elliptic curve over a fixed prime field varies,” J. London Math. Soc., 43(1):57–60 (1968).Google Scholar
  158. 158.
    B. J. Birch, “Weber's class invariants,” Mathematika, 16(2):283–294 (1969).Google Scholar
  159. 159.
    B. J. Birch, “Diophantine analysis and modular functions,” Algebr. Geom. London, 35–42 (1969).Google Scholar
  160. 160.
    B. J. Birch and K. McCann, “A criterion for the p-adic solvability of Diophantine equations,” Quart. J. Math., 18(69):59–63 (1967).Google Scholar
  161. 161.
    B. J. Birch and N. M. Stephens, “The parity of the rank of the Mordell-Weil group,” Topology, 5(4):295–299 (1966).Google Scholar
  162. 162.
    B. J. Birch and H. P. F. Swinner ton-Dyer, “Notes on elliptic curves. II,” J. reine und angew. Math., 218:79–108 (1965).Google Scholar
  163. 163.
    F. van der Blij, “Methodes algébriques et analytiques dans la théorie des nombres,” Bull. Soc. math. Belg., 15(1):13–17 (1963).Google Scholar
  164. 164.
    E. Bombieri, “Sull'analogo della formula di Selberg nei corpi di funzioni,” Atti Accad. naz. Lincei. Rend. Cl. sci. fis., mat. e natur., 35(5):252–257 (1963).Google Scholar
  165. 165.
    E. Bombieri, “On Galois coverings over finite fields,” Actas Coloq. internac. geometria algebraica. Madrid, 1965. Madrid, 23–30 (1965).Google Scholar
  166. 166.
    E. Bombieri, “Nuovi risultati sulla geometria di una ipersuperficie cubica a tre dimensioni,” Simpos. internaz. geometria algebraica, Roma, 1965. Roma, 22–28 (1967).Google Scholar
  167. 167.
    E. Bombieri, “On exponential sums in finite fields,” Colloq. Centre nat. rech. scient., 143:37–41 (1966).Google Scholar
  168. 168.
    E. Bombieri, “Nuovi risultati sulla geometria di una ipersuperficie cubica a tre dimension,” Rend. mat. e applic., 25(1–2):22–28 (1966).Google Scholar
  169. 169.
    E. Bombieri and H. P. F. Swinnerton-Dyer, “On the local zeta-function of a cubic threefold,” Ann. Scuola norm. super. Pisa Sci. fis. e mat., 21(1):1–29 (1967).Google Scholar
  170. 170.
    A. Borel and J.-P. Serre, “Théoremes de finitude en cohomologie galoisienne,” Comment. math. helv., 39(2):111–164 (1964).Google Scholar
  171. 171.
    J. Browkin, “On forms over p-adic fields,” Bull. Acad. polon. sci. Ser. math., astron. et phys., 14(9):489–492 (1966).Google Scholar
  172. 172.
    F. Bruhat, “Points entiers sur les courbes de genre≥1.” Semin Bourbaki. Secret. math., 15(2):247/01–247/12 1962–1963 (1964).Google Scholar
  173. 173.
    M. Brynski, “O formach rozmaitosci algebraicznych,” Roczh. Polsk. towarz. mat., 10(2):119–129 Ser. 1, (1966).Google Scholar
  174. 174.
    J. Brzezinski, “On relatively minimal models of fields of genus 0,” Bull. Acad. polon. sci. Sér. sci. math., astron. et phys., 16(5):375–382 (1968).Google Scholar
  175. 175.
    J. Brzezinsk, “Models for some fields of genus 0 determined by forms,” Bull. Acad. polon. sci. Sér. sci. math., et phys., 17(8):473–475 (1969).Google Scholar
  176. 176.
    I. Bucur, “Sur la formule de Weil en cohomologie étale” Rev. roumaine math. pures et appl., 12(9):1145–1147(1967).Google Scholar
  177. 177.
    A. Buquet, “A propos des points rationnels des cubiques,” Bull. Assoc. professeurs math. enseign. public, 47(260):24–28 (1968).Google Scholar
  178. 178.
    P. Cartier, “Groupes algébriques et groupes formels,” Colloq. théor. groupes algébr. Bruxelles, 1962. Louvain-Paris, 87–110 (1962).Google Scholar
  179. 179.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. I,” On a conjecture of Selmer. J. reine und angew. Math., 202(1–2):52–99 (1959).Google Scholar
  180. 180.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. II,” A general result. J. reine und angew. Math., 203(3–4):174–208 (1960).Google Scholar
  181. 181.
    J. W. S. Cassels, “Arithmetic on an elliptic curve,” Proc. Internat. Congr. Math. Aug. 1962, Djursholm. Uppsala, 234–246 (1963).Google Scholar
  182. 182.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. III,” The Tate-Safarevic and Selmer groups. Proc. London Math. Soc., 12(46):259–296 (1962).Google Scholar
  183. 183.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. IV,” Proof of the Hauptvermutung. J. reine und angew. Math., 211(1–2):95–112 (1962).Google Scholar
  184. 184.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. III,” The Tate-Safarevic and Selmer groups. Corrigendum. Proc. London Math. Soc., 13(52):768 (1963).Google Scholar
  185. 185.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. V,” Two counter-examples,” J. London Math. Soc., 38(2):244–248 (1963).Google Scholar
  186. 186.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. VI,” The Tate-Safarevic group can be arbitrarily large. J. reine und angew. Math., 214–215:65–70 (1964).Google Scholar
  187. 187.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. VII,” The dual exact sequence. J. reine und angew. Math., 216(3–4):150–158 (1964).Google Scholar
  188. 188.
    J. W. S. Cassels, “Arithmetic on Abelian varieties especially of dimension 1,” Lect. Notes. Amer. Math. Soc. and Summer Inst. Alg. Geometry, Woods Hole, Mass., 1964, S. 1., s. a., 1–10.Google Scholar
  189. 189.
    J. W. S. Cassels, “Arithmetic on curves of genus 1. VIII,” On conjectures of Birch and Swinnerton-Dyer. J. reine and angew. Math., 217:180–199 (1965).Google Scholar
  190. 190.
    J. W. S. Cassels, “Integral points on certain elliptic curves,” Proc. London Math. Soc., 14a:55–57 (1965).Google Scholar
  191. 191.
    J. W. S. Cassels, “Diophantine equations with special reference to elliptic curves,” J. London Math. Soc., 41(2):193–291 (1966).Google Scholar
  192. 192.
    J. W. S. Cassels, “Elliptic curves over local fields,” Proc. Conf. Local fields, Driebergen, 1966. Berlin-Heidelberg-New York, 37–39 (1967).Google Scholar
  193. 193.
    J. W. S. Cassels, “On a theorem of Dem'janenko,” J. London Math. Soc., 43(1):61–66 (1968).Google Scholar
  194. 194.
    J. W. S. Cassels and M. J. T. Guy, “On the Hasse principle for cubic surfaces,” Mathematika, 13(2):111–120 (1966).Google Scholar
  195. 195.
    F. Chatelet, “Points rationnels sur certaines surfaces cubiques,” Colloq. intern. Centre nat. rech. scient., 143:67–75 (1966).Google Scholar
  196. 196.
    S. Chowla, “On a conjecture of Artin. I, II,” Kgl. norske vid. selskabs forhandl., No. 29, 135–138; No. 30, 139–141 (1963).Google Scholar
  197. 197.
    S. Chowla, “The Riemann hypothesis and Hilbert's tenth problem,” Kgl. norske vid. selskabs. forhandl., 38(14):62–64 (1965).Google Scholar
  198. 198.
    S. Chowla, “The Riemann hypothesis and Hilbert's tenth problem,” New York, Gordon and Breach, 1965, XV, p. 119.Google Scholar
  199. 199.
    S. Chowla, “On the class-number of the function-field y2=f(x) over GF(p),” Kgl. norske vid. selskabs. forhandl., 39(14):86–88 1966 (1967).Google Scholar
  200. 200.
    S. Chowla, “On the class-numbers of some function-fields: y2=f(x) over GF(p),” ILI Kgl. norske vid. selskabs forhandl., 40(2):7–10 (1967).Google Scholar
  201. 201.
    S. Chowla and H. Hasse, “On a paper of Bombieri,” Kgl. norske vid. selskab. forhandl, 41(8):30–33 (1968).Google Scholar
  202. 202.
    J. Coates, “Approximation in algebraic function fields of one variable,” J. Austral. Math. Soc., 7(3):341–355 (1967).Google Scholar
  203. 203.
    J. Coates, “An effective p-adic analogue of a theorem of Thue,” Acta arithm., 15(3):279–305 (1969).Google Scholar
  204. 204.
    Colloque sur la théorie des groupes algebriques. Tenu á Bruxelles 5–7 juin 1962. CBRM. Louvain, Libr. Univ., Paris, Gauthier-Villars, 1962, p. 150.Google Scholar
  205. 205.
    I. Connell, “Abelian formal groups,” Proc. Amer. Math. Soc., 17(4):958–959 (1966).Google Scholar
  206. 206.
    M. Davis, “Diophantine equations and recursively enumerable sets,” Automata theory. New York-London, Acad. Press, 146–152 (1966).Google Scholar
  207. 207.
    M. Davis and H. Putnam, “Diophantine sets over polynomial rings,” Illinois J. Math., 7(2):251–256 (1963).Google Scholar
  208. 208.
    P. Deligne, “Formes modulaires et représentationsl-adiques,” Semin. Bourbaki, 21 annee, 1968/69, 355/01–355/34; Lect. Notes Math., 179:1392-172 (1971).Google Scholar
  209. 209.
    P. Deligne, “Variétés abéliennes ordinaires sur un corps fini,” Invent. Math., 8(3):238–243 (1969).Google Scholar
  210. 210.
    F. Delmer, “Equations diophantiennes et géométrie des courbes,” Sémin. Délange-Pisot-Poitou. Theor. nombres. Fac. sci. Paris, 10(2):19/01–19/16 (1968–1969).Google Scholar
  211. 211.
    J. Dieudonné, “Group schemes and formal groups,” Actas Coloq. internac. geometriá algebraica. Madrid, 1965. Madrid, 57–67 (1965).Google Scholar
  212. 212.
    J. Dieudonné, “Hyperalgebres et groupes formels,” Semin. 1962–1963 analisi, algebra, geometria e topol., vol. 2. Roma, 512–524 (1965).Google Scholar
  213. 213.
    Dix exposés sur la cohomologie des schémas (Advanced Stud. Pure Math., vol. 3) Amsterdam, North-Holland Publ. Co., Paris, Masson et Cie, ed., 1968, p. 386.Google Scholar
  214. 214.
    K. Doi, “On the jacobian varieties of the fields of elliptic modular functions,” Osaka Math. J., 15(2):249–256 (1963).Google Scholar
  215. 215.
    K. Doi, “On the field of moduli of an abelian variety with complex multiplication,” J. Math. Soc. Japan, 15(3):237–243 (1963).Google Scholar
  216. 216.
    K. Doi and H. Naganuma, “On the jacobian varieties of the fields of elliptic modular functions. II,” J. Math. Kyoto Univ., 6(2):177–185 (1967).Google Scholar
  217. 217.
    K. Doi and H. Naganuma, “On the algebraic curves uniformized by arithmetical automorphic functions,” Ann. Math., 86(3):449–460 (1967).Google Scholar
  218. 218.
    A. Douady, “Détermination d'un groupe de Galois,” C.r. Acad. sci., 258(22):5305–5308 (1964).Google Scholar
  219. 219.
    B. Dwork, “On the zeta-function of a hypersurface,” Publs math. Inst. hautes études scient., 12:5–68 (1962).Google Scholar
  220. 220.
    B. Dwork, “A deformation theory for the zeta-function of a hypersurface,” Proc. Internat. Congr. Math. Aug. 1962, Djursholm. Uppsala, 247–259 (1963).Google Scholar
  221. 221.
    B. Dwork, “On the zeta-function of a hypersurface. II,” Ann. Math., 80(2):227–299 (1964).Google Scholar
  222. 222.
    B. Dwork, “Some remarks concerning the zeta-function of an algebraic variety over a finite field,” Lect. Notes. Amer. Math. Soc. and Summer Inst. Algebr. Geometry, Woods Hole, Mass., 1964, S. 1, s. a., 1–8.Google Scholar
  223. 223.
    B. Dwork, “Analytic theory of the zeta-function of algebraic varieties,” Arithmet. algebraic geometry. Proc. Conf., Purdue Univ., 1963, New York, 18–32 (1965).Google Scholar
  224. 224.
    B. Dwork, “On zeta-functions of hypersurfaces,” Colloq. internat. Centre nat. rech. scient., 143:77–82 (1966).Google Scholar
  225. 225.
    B. Dwork, “On the zeta-function of a hypersurface. III,” Ann. Math., 83(3):457–519 (1966).Google Scholar
  226. 226.
    B. Dwork, “On the rationality of zeta-functions and L-series,” Proc. Conf. Local fields. Driebergen, 1966. Berlin-Heidelberg-New York, 40–55 (1967).Google Scholar
  227. 227.
    M. Eichler, “Einführung in die Theorie der algebraischen Zahlen und Funktionen,” Basel-Stuttgart, Birkhauser Verl., 1963, 338S.Google Scholar
  228. 228.
    N. C. Fincke, “Abelian threefolds,” Doct. diss. Univ. Pittsburgh, 1966, 78 pp. Dissert. Abstrs, B27(7):2440–2441 (1967).Google Scholar
  229. 229.
    I. Fischer, “On the specialization of birationally equivalent curves,” Amer. J. Math., 85(2):151–155 (1963).Google Scholar
  230. 230.
    A. Frolich, “Quadratic forms á. la'local theory,” Proc. Cambridge Philos. Soc., 63(3):579–586 (1967).Google Scholar
  231. 231.
    W. E. Fulton, “The fundamental group of an algebraic curve,” Doct. diss. Princeton Univ., 1966, p. 71. Dissert. Abstrs., B27(6):2025 (1966).Google Scholar
  232. 232.
    Y. Furuta and Y. Sawada, “On the Galois cohomology group of the ring of integers in a global field and its adele ring,” Nagoya Math. J., 32:247–252, June (1968).Google Scholar
  233. 233.
    J. Gamst, “Quaternions généralisés,” C. r. Acad. Sci., 269(14):A560-A562 (1969).Google Scholar
  234. 234.
    P. Gerl, “Punktfolgen auf Kurven und Flachen,” Monatsh. Math., 67(5):401–432 (1963).Google Scholar
  235. 235.
    J. Giraud, “Remarque sur une formule de Shimura-Taniyama,” Invent, math., 5(3):231–236 (1968).Google Scholar
  236. 236.
    L. J. Goldstein, “The analytic theory of zeta-functions associated to automorphic forms,” Doct. diss. Princeton Univ., 1967, 102 pp. Dissert. Abstrs., B28(8):3377 (1968).Google Scholar
  237. 237.
    H. Grauert, “Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkorper,” Publs math. Inst. hautes études scient., 25:363–381 (1965).Google Scholar
  238. 238.
    H. Grauert and R. Remmert, “Nichtarchimedische Funktionentheorie,” Wiss. Abhandl. Arbeitsgemeinsch. Forsch. Landes Nordthein-Westfalen, 33:393–476 (1966).Google Scholar
  239. 239.
    W. H. Graver, “Divisibility of the group of divisor classes of degree zero of an elliptic curve,” Doct. diss. Ind. Univ., 1966, p. 36. Dissert. Abstrs, B27(10):3595 (1967).Google Scholar
  240. 240.
    M. J. Greenberg, “Schemata over local rings,” Ann. Math., 73(3):624–648 (1961).Google Scholar
  241. 241.
    M. J. Greenberg, “Schemata over local rings. II,” Ann. Math., 78(2):256–266 (1963).Google Scholar
  242. 242.
    M. J. Greenberg, “Rational points in Henselian discrete valuation rings,” Bull. Amer. Math. Soc., 72(4):713–714 (1966).Google Scholar
  243. 243.
    M. J. Greenberg, “Rational points in Henselian discrete valuation rings,” Publs math. Inst. hautes études scient, 31:563–568 1966(1967).Google Scholar
  244. 244.
    M. J. Greenberg, “Lectures on forms in many variables,” Benjamin, New York, 1969.Google Scholar
  245. 245.
    N. Greenleaf, “Irreducible subvarieties and rational points,” Amer. J. Math., 87(1):25–31 (1965).Google Scholar
  246. 246.
    A. Grothendieck, “Géométrie formelle et Géométrie algébrique,” Semin. Gourbaki. Secrét, math. 1958–1959, 11 année, fasc. 3, Paris, 182/1–182/28 (1959).Google Scholar
  247. 247.
    A. Grothendieck, “Formule de Lefschetz et rationalité des fonctions L,” Sémin. Bourbaki. Secrét, math., 17(1):279-01–279-15 1964–1965(1966). Dix exposes cohomol. schémas. Amsterdam-Paris, 31–45 (1968).Google Scholar
  248. 248.
    A. Grothendieck, “Un théoréme sur les homomorphismes de schémas abeliens,” Invent. math., 2(1):59–78 (1966).Google Scholar
  249. 249.
    A. Grothendieck, “Le groupe de Brauer Sémin,” Bourbaki. Secrét, math., 17(3):290-01–290-21 1964–1965 (1966).Google Scholar
  250. 250.
    A. Grothendieck, “Le groupe de Brauer. II,” Dix exposés cohomol. shemas. Amsterdam-Paris, 67–87 (1968).Google Scholar
  251. 251.
    A. Grothendieck, “Le groupe de Brauer. III,” Examples et compléments. Dix exposés cohomol. schémas. Amsterdam-Paris, 88–188 (1968).Google Scholar
  252. 252.
    A. Grothendieck, “Classes de Chern et representations lineaires des groupes discrets,” Dix exposés cohomol. schémas. Amsterdam-Paris, 215–305 (1968).Google Scholar
  253. 253.
    H. Hasse, “Zahlentheorie. 2 erw,” Aufl. Berlin, Akad.-Verl., 1963, XVI, 611S.Google Scholar
  254. 254.
    H. Hasse, “Modular functions and elliptic curves over finite fields,” Sirapos. internaz. geometria algebrica, Roma, 1965. Roma, 248–266 (1967).Google Scholar
  255. 255.
    H. Hasse, “Modular functions and elliptic curves over finite fields,” Rend. mat. e applic., 25(1–2):248–266 1966(1967).Google Scholar
  256. 256.
    T. Hayashida, “A class number associated with a product of two elliptic curves,” Natur. Sci. Rept. Ochanomizu Univ., 16(1):9–19 (1965).Google Scholar
  257. 257.
    T. Hayashida, “A class number associated with the product of an elliptic curves with itself,” J. Math. Soc. Japan, 20(1–2):26–43 (1968).Google Scholar
  258. 258.
    J. P. Heisler, “Diophantine problems for matrix rings, rings of functions, and other rings,” Doct. diss. Univ. Mich., 1965, p. 71. Dissert. Abstrs, 26(11):6471 (1966).Google Scholar
  259. 259.
    Y. Hellegouarch, “Une propriété arithmétique des points exceptionnels rationnels d'ordre pair d'une cubique de genre 1. C. r. Acad. sci., 260(23):5989–5992 (1965).Google Scholar
  260. 260.
    Y. Hellegouarch, “Applications d'une propriété arithmétique des points exceptionnels d'orde pair d'unecubique de genre 1 C. r,”. Acad. sci., 260(24):6256–6258 (1965).Google Scholar
  261. 261.
    Y. Hellegouarch, “Application de la théorie des fonctions théta á un probléme de théorie des nombres,” C. r. Acad. Sci., 269(19):A883-A884 (1969).Google Scholar
  262. 262.
    T. Hiramatsu, “Modular forms obtained from L-functions with Grossen-characters of Q(√−3). Comment. math. Univ. St. Pauli, 14(2):65–70 (1966).Google Scholar
  263. 263.
    K. Hoechsmann, “Zahlentheorie (insbesondere algebraische Zahlentheorie),” Math. Forschungsinst. Oberwolfach., 11S (1964).Google Scholar
  264. 264.
    T. Honda, “On the Jacobian variety of the algebraic curve y2=1−x1 over a field of characteristic p> 0,” Osaka J. Math., 3(2):189–194 (1966).Google Scholar
  265. 265.
    T. Honda, “Formal groups and zeta-functions,” Osaka J. Math., 5(2):199–213 (1968).Google Scholar
  266. 266.
    T. Honda, “Isogeny classes of abelian varieties over finite fields,” J. Math. Soc. Japan, 20(1–2):83–95 (1968).Google Scholar
  267. 267.
    J.-I. Igusa, “Structure theorems of modular varieties,” Proc. Internat. Congr. Math. Aug. 1962, Djursholm. Uppsala, 522–525 (1963).Google Scholar
  268. 268.
    J.-I. Igusa, “On the algebraic theory of elliptic modular functions,” J. Math. Soc. Japan, 20(1–2):96–106 (1968).Google Scholar
  269. 269.
    Y. Ihara, “On the discrete subgroups of the two by two projective linear group over p-adic fields,” J. Math. Soc. Japan, 18(3):219–235 (1966).Google Scholar
  270. 270.
    Y. Ihara, “Hecke polynomials as congruence ξ-functions in elliptic modular case,” Ann. Math., 85(2):267–295 (1967).Google Scholar
  271. 271.
    Y. Ihara, “The congruence monodromy problems,” J. Math. Soc. Japan, 20(1–2):107–121 (1968).Google Scholar
  272. 272.
    K. F. Ireland, “On the zeta-function of an algebraic variety,” Amer. J. Math., 89(3):643–660 (1967).Google Scholar
  273. 273.
    M. Ishida, “On rational points of homogeneous spaces over finite fields,” J. Math. Soc. Japan, 20(1-2):122–129 (1968).Google Scholar
  274. 274.
    H. Jacques and R. P. Langlands, “Automorphic forms on GL(2),” Lect. Notes Math., 1970, 114, VII, p. 548.Google Scholar
  275. 275.
    M. Jarden, “Rational points on algebraic varieties over large number fields,” Bull. Amer. Math. Soc., 75(3):603–606 (1969).Google Scholar
  276. 276.
    K. Katayama, “On the Hilbert-Siegel modular group and abelian varieties,” J. Fac. Sci, Univ. Tokyo, 9(3):261–291 (1962). Sec. 1.Google Scholar
  277. 277.
    K. Katayama, “On the Hilbert-Siegel modular group and abelian varieties. II,” J. Fac. Sci. Univ. Tokyo, 9(5):433–467 (1963). Sec. 1.Google Scholar
  278. 278.
    N. Katz, “On the differential equations satisfied by period matrices,” Publs math. Inst. hautes études scient., 35:223–258 1968(1969).Google Scholar
  279. 279.
    V. J. Katz, “The Brauer group of a regular local ring,” Doct. diss. Brandeis Univ., 1968, p. 79. Dissert. Abstrs., B29(8):2976–2977 (1969).Google Scholar
  280. 280.
    E. F. Kennel, “Class field theory in dimension greater than one,” Doct. diss. Univ. Ore., 1965, p. 68. Dissert. Abstrs, 26(9):5462 (1966).Google Scholar
  281. 281.
    S. L. Kleiman, “Algebraic cycles and the Weil conjectures,” Dix exposés cohomol. schémas. Amsterdam-Paris, 359–386 (1968).Google Scholar
  282. 282.
    H. Koch, “Über die Galoissche Gruppe der algebraischen Abschiessungeines Potenzreihenkorpers mit endlichem Konstantenkorper,” Math. Nachr., 35(5–6):323–327 (1967).Google Scholar
  283. 283.
    S. Konno, “On Artin's L-functions of the algebraic curves uniformized by certain automorphic functions,” J. Math. Soc. Japan, 15(1):89–100 (1963).Google Scholar
  284. 284.
    T. Kubota, “An application of the power residue theory to some abelian functions,” Nagoya Math. J., 27(1):51–54 (1966).Google Scholar
  285. 285.
    M. Kuga and G. Shimura, “On the zeta-function of a fibre variety whose fibres are abelian varieties,” Ann. Math., 82(3):478–539 (1965).Google Scholar
  286. 286.
    W. Kuyk, “Extensions de corps hilbertiens,” J. Algebra, 14(1):112–124 (1970).Google Scholar
  287. 287.
    S. Lang, “Diophantine geometry,” New York, Intersci. Publ., 1962, p. 170.Google Scholar
  288. 288.
    S. Lang, “Transcendental points on group varieties,” Topology, 1:313–318 (1962). Oct–Dec.Google Scholar
  289. 289.
    S. Lang, “Les formes bilinéaires de Neron et Tate,” Sémin. Bourbaki. Secrét, math., 16(3):274/01–274/11 (1967).Google Scholar
  290. 290.
    S. Lang, “Diophantine approximations on toruses,” Amer. J. Math., 86(3):521–533 (1964).Google Scholar
  291. 291.
    S. Lang, “Division points on curves,” Ann. mat. pura ed. appl., 70:229–234 (1965).Google Scholar
  292. 292.
    S. Lang, “Algebraic values of meromorphic functions,” Topology, 3(2):183–191 (1965).Google Scholar
  293. 293.
    S. Lang, “Algebraic values of meromorphic functions. II,” Topology, 5(4):363–370 (1966).Google Scholar
  294. 294.
    R. P. Langlands, “Problems in the theory of automorphic forms,” Lect. Notes Math., 170:18–61 (1970).Google Scholar
  295. 295.
    M. Lazard, “Groupes analytiques p-adiques,” Publs math. Inst. hautes études scient., 1965, No: 26, p. 219.Google Scholar
  296. 296.
    Lecture Notes. American Mathematical Society and Summer Institute on Algebraic Geometry. Woods Hole, Mass., July 6–31, 1964. S. 1., s. a., p. 237.Google Scholar
  297. 297.
    J. R. C. Leitzel, “On the group of divisor classes of degree zero of an algebraic curve,” Doct. diss. Ind. Univ., 1965, p. 41. Dissert. Abstrs., 26(11):6743–6744 (1966).Google Scholar
  298. 298.
    J. R. C. Leitzel, “Galois cohomology and class number in constant extension of algebraic function fields,” Proc. Amer. Math. Soc., 22(1):206–208 (1969).Google Scholar
  299. 299.
    M. Levin, “On the group of rational points on elliptic curves over function fields,” Amer. J. Math., 90(2):456–460 (1968).Google Scholar
  300. 300.
    S. Lichtenbaum, “Curves over discrete valuation rings,” Amer. J. Math., 90(2):380–405 (1968).Google Scholar
  301. 301.
    S. Lichtenbaum, “The period-index problem for elliptic curves,” Amer. J. Math., 90(4):1209–1223 (1968).Google Scholar
  302. 302.
    S. Lichtenbaum, “Duality theorems for curves over p-adic fields,” Invent. math., 7(2):120–136 (1969).Google Scholar
  303. 303.
    J. Lubin, “One-parameter formal Lie groups over p-adic integer rings,” Ann. Math., 80(3):464–484 (1964).Google Scholar
  304. 304.
    J. Jubin, “Correction to ‘One-parameter formal Lie groups over p-adic integer rings,’” Ann. Math., 84(2):372 (1966).Google Scholar
  305. 305.
    J. Lubin, “Finite subgroups and isogenies of one-parameter formal Lie groups,” Ann. Math., 85(2):296–302 (1967).Google Scholar
  306. 306.
    J. Lubin and J. Tate, “Formal complex multiplication in local fields,” Ann. Math., 81(2):380–387 (1965).Google Scholar
  307. 307.
    J. Lubin and J. Tate, “Formal moduli for one-parameter formal Lie groups,” Bull. Soc. math. France, 94(1):49–59 (1966).Google Scholar
  308. 308.
    S. Lubkin, “On a conjecture of Andre Weil,” Amer. J. Math., 89(2):443–548 (1967).Google Scholar
  309. 309.
    S. Lubkin, “A p-adic proof of Weil's conjectures,” Ann. Math., 87(1):105–194 (1968).Google Scholar
  310. 310.
    S. Lubkin, “A result on the Weil zeta-function,” Trans. Amer. Math. Soc., 139:297–300 (1969). May.Google Scholar
  311. 311.
    M. L. Madan, “On the Galois cohomology of tamely ramified fields of algebraic functions,” Arch. Math., 17(5):400–408 (1966).Google Scholar
  312. 312.
    Yu. I. Manin [J. I. Manin], “Moduli fuchsiani,” Ann. Scuola norm. super. Pisa Sci. fis. et mat., 19(1):113–126 (1965).Google Scholar
  313. 313.
    Yu. I. Manin [J. I. Manin], “Two theorems on rational surfaces,” Rend. mat. e applic., 25(1–2):198–207 1966(1967).Google Scholar
  314. 314.
    Yu. I. Manin [J. I. Manin], “Hyper surfaces cubiques. II,” Automorphismes birationnels en dimension deux. Invent. math., 6(4):334–352 (1969).Google Scholar
  315. 315.
    T. Matsui, “On the endomorphism algebra of jacobian varieties attached to the fields of elliptic modular functions,” Osaka J. Math., 1(1):25–31 (1964).Google Scholar
  316. 316.
    B. Mazur and L. Roberts, “Local Euler characteristics,” Invent. math., 9(3):201–234 (1970).Google Scholar
  317. 317.
    A. Menalda, “Representations of modulary congruence groups,” Proc. Koninkl. nederl. akad. wet., A68(5):760–767 (1965). Indagationes math., 27(5):760–767 (1965).Google Scholar
  318. 318.
    J. Milne, “Extensions of abelian varieties defined over a finite field,” Invent. math., 5(1):63–84 (1968).Google Scholar
  319. 319.
    J. Milne, “The Tate-Safarevic group of a constant abelian variety,” Invent. math., 6(1):91–105 (1968).Google Scholar
  320. 320.
    M. Miwa, “On Mordell's conjecture for algebraic curves over function fields,” J. Math. Soc. Japan, 18(2):182–188 (1966).Google Scholar
  321. 321.
    M. Miwa, “On Mordell's conjecture for the curve over function field with arbitrary constant field,” J. Math. Soc. Japan, 21(2):229–233 (1969).Google Scholar
  322. 322.
    M. Miwa, “Galois cohomology and birational invariant of algebraic varieties,” J. Math. Soc. Japan, 21(4):584–603 (1969).Google Scholar
  323. 323.
    L. J. Mordell, “Rownanie diofantyczne y2=ax3+bx2+cx+d. Roczn. Polsk. towarz. mat., 7(2):203–210 (1964). Ser. 2.Google Scholar
  324. 324.
    L. J. Mordell, “Diophantine equations,” London, Acad. Press, 1969, X, p. 312.Google Scholar
  325. 325.
    M. Mori, “Über die rationale Darstellbarkeit der Heckeschen Operatoren,” J. Math. Soc. Japan, 15(3):256–267 (1963).Google Scholar
  326. 326.
    H. Morikawa, “Theta-functions and abelian varieties over valuation fields of rank one. I,” Nagoya Math. J., 20:1–27 (1962).Google Scholar
  327. 327.
    H. Morikawa, “On theta-functions and abelian varieties over valuation fields of rank one. II, Theta functions and abelian functions of characteristic p>(0),” Nagoya Math. J., 21:231–250 (1962). Dec.Google Scholar
  328. 328.
    Y. Morita, “Hecke polynomials Hkp(u) (p=2 or 3),” J. Fac. Sci. Univ. Tokyo, 15(1):99–105 (1968). Sec. 1.Google Scholar
  329. 329.
    Y. Morita, “Hecke polynomials of modular groups and congruence zeta-functions of fibre varieties,” J. Math. Soc. Japan, 21(4):617–637 (1969).Google Scholar
  330. 330.
    D. Mumford, “A remark on Mordell's conjecture,” Amer. J. Math., 87(4):1007–1016 (1965).Google Scholar
  331. 331.
    D. Mumford, “A note to Shimura's paper ‘Discontinuous groups and Abelian varieties,’” Math. Ann., 181(4):345–351 (1969).Google Scholar
  332. 332.
    T. Murasaki, “On rational cohomology classes of type (p, p) on an Abelian variety,” Sci. Rets Tokyo Kyoiku Daigaku, A10(232–248):66–74 (1969).Google Scholar
  333. 333.
    A. Nerode, “A decision method for p-adic integral zeros of diophantine equations,” Bull. Amer. Math. Soc., 69(4):513–517 (1963).Google Scholar
  334. 334.
    A. Néron, “Modéles minimaux des variétés abéliennes sur les corps locaux et globaux,” Publs math. Inst. hautes études scient., 1964, No. 21, p. 128.Google Scholar
  335. 335.
    A. Néron, “Hauteurs des points rationnels d'une variéte abélienne définie sur un corps global,” Actas Coloq. internac. geometría algebraica. Madrid, 1965. Madrid, 49–56 (1965).Google Scholar
  336. 336.
    A. Neron, “Quasi-fonctions et hauterus sur les variéties abéliennes,” Ann. Math., 82(2):249–331 (1965).Google Scholar
  337. 337.
    A. Neron, “Dege d'intersection en géométrie diophantienne,” in: Internat. Congr. Mathematicians. Report Abstracts [in Russian], Moscow (1966), pp. 71–81.Google Scholar
  338. 338.
    A. Néron, “Modeles minimaux des espaces principaux homogénes sur les courbes elliptiques,” Proc. Conf. Local Fields, Driebergen, 1966. Berlin-Heidelberg-New York, 66–77 (1967).Google Scholar
  339. 339.
    A. Neron, “Degre d'intersection en géométrie diophantienne,” in: Internat. Congr. Mathematicians. Report Abstracts [in Russian], Moscow (1966), pp. 485–495.Google Scholar
  340. 340.
    A. Néron, “Modéles minimaux et différentielles,” Sympos. math. Vol. 3. Roma, 279–293 (1970).Google Scholar
  341. 341.
    O. Neumann, “Zur Galois-Kohomologie Abelsher Mannigfaltigkeiten,” Math. Nachr., 40(4–6):367–378 (1969).Google Scholar
  342. 342.
    N. Nobusawa, “On rationality of algebraic function fields,” Canad. Math. Bull., 12(3):339–341 (1969).Google Scholar
  343. 343.
    A. P. Ogg, “Cohomology of Abelian varieties over function fields,” Ann. Math., 76(2):185–212 (1962).Google Scholar
  344. 344.
    A. P. Ogg, On Pencils of Curves of Genus Two, Topology, 5(4):355–362 (1966).Google Scholar
  345. 345.
    A. P. Ogg, “Abelian curves of 2-power conductor,” Proc. Cambridge Philos. Soc., 62(2):143–148 (1966).Google Scholar
  346. 346.
    A. P. Ogg, “Abelian curves of small conductor,” J. reine und angew. Math., 226:204–215 (1967).Google Scholar
  347. 347.
    A. P. Ogg, “Elliptic curves and wild ramification,” Amer. J. Math., 89(1):1–21 (1967).Google Scholar
  348. 348.
    A. P. Ogg, “On a convolution of L-series,” Invent. math., 7(4):297–312 (1969).Google Scholar
  349. 349.
    A. P. Ogg, “A remark on the Sato-Tate conjecture,” Invent. math., 9(3):198–200 (1970).Google Scholar
  350. 350.
    L. D. Olson, “The group CkkDk and the period-index problem in WC groups,” Doct. diss. Columbia Univ., 1968, 33 pp. Dissert. Abstrs., B29(6):2121 (1968).Google Scholar
  351. 351.
    O. T. O'Meara, “Introduction to quadratic forms,” Berlin, Springer (1963), p. 342.Google Scholar
  352. 352.
    O. T. O'Meara, “On the Tamagawa number of algebraic tori,” Ann. Math., 78(1):47–73 (1963).Google Scholar
  353. 353.
    O. T. O'Meara, “On the relative theory of Tamagawa numbers,” Bull. Amer. Math. Soc., 70(2):325–326 (1964).Google Scholar
  354. 354.
    O. T. O'Meara, “The Gauss-Bonnet theorem and the Tamagawa number,” Bull. Amer. Math. Soc., 71(2):345–348 (1965).Google Scholar
  355. 355.
    O. T. O'Meara, “On the relative theory of Tamagawa numbers,” Ann. Math., 82(1):88–111 (1965).Google Scholar
  356. 356.
    O. T. O'Meara, “On Tamagawa numbers,” in: Internat. Congr. Mathematicians. Report Abstracts [in Russian], Moscow (1966), pp. 81–82.Google Scholar
  357. 357.
    O. T. O'Meara, “On Tamagawa numbers,” Proc. Internat. Congr. Mathematicians 1966 [in Russian], “Mir,” Moscow (1968), pp. 509–512.Google Scholar
  358. 358.
    O. T. O'Meara, “An integral attached to a hypersurface,” Amer. J. Math., 90(4):1223–1236 (1968).Google Scholar
  359. 359.
    O. T. O'Meara, “A mean value theorem in adele geometry,” J. Math. Soc. Japan, 20(1–2):275–288 (1968).Google Scholar
  360. 360.
    F. Ourt, “Commutative group schemes,” New York, Springer (1966), var. P21., ill.; Publisher's Weekly, 190(3):103 (1966).Google Scholar
  361. 361.
    F. Ourt and D. Mumford, “Deformations and liftings of finite, commutative group schemes,” Invent. math., 5(4):317–334 (1968).Google Scholar
  362. 362.
    C. Pisot, “L'analyse p-adique en théorie des nombres,” Sémin. théor. nombres Delange-Pisot. Fac. sci. Paris, 1963–1964, 5(1):1–6 (1967).Google Scholar
  363. 363.
    H. J. Pohlmann, “On the zeta-function of an Abelian variety of complex multiplication type,” Doc. diss. Berkeley, Univ. California (1965), p. 59. Dissert. Abstrs. 26(2):1071 (1965).Google Scholar
  364. 364.
    H. J. Pohlmann, “Algebraic cylces on Abelian varieties of complex multiplication type,” Ann. Math., 88(1):161–180 (1968).Google Scholar
  365. 365.
    G. Poitou, “Points rationalles sur les courbes,” Semin. P. Dubreil, Moscow-Leningrad, Dubreil-Ja-cotin et C. Pisot; Fac. Sci. Paris, 1960–1961, 14, fasc. 2, Paris, 1963, 21/01–21/12.Google Scholar
  366. 366.
    H. Popp, “Zur Reduktionstheorie algebraischer Funktionenkorper vom Transzendenzgrad 1: Existenz einer regularen Reuktion zu vorgegebenem Funktionenkorper als Restklassenkorper,” Arch. Math., 17(6):510–522 (1966).Google Scholar
  367. 367.
    H. Popp, “Über die Fundamentalgruppe einer punktierten Riemannschen Flächen bei Charakteristik p>0,” Math. Z., 96(2):111–124 (1967).Google Scholar
  368. 368.
    H. Popp, “Über des Verhalten des Geschlech eines Funktonenkoprpers einer Variablen bei Konstantenreduktion,” Math. Z., 106(1):17–35 (1968).Google Scholar
  369. 369.
    Y. Pourchet, “Formes cubiques sur les corps locaux,” Sémin. théor. nombres Delange-Pisto, Fac. sci. Paris, 1965–1966 (1967), 7, fasc. 2, No. 18, 1–9.Google Scholar
  370. 370.
    Proceedings of a Conference on Local Fields, NUFFIC Summer School, Driebergen, 1966. Ed. Springer T. A. Berlin-Heidelberg-New York, Springer (1967), p. 214.Google Scholar
  371. 371.
    S. Raghavan and S. Rangachari, “On zeta-functions of quadratic forms,” Ann. Math., 85(1):46–57 (1967).Google Scholar
  372. 372.
    A. R. Rajwade, “Arithmetic on curves with complex multiplication by (-2)1/2,” Proc. Cambridge Philos. Soc., 64(3):659–672 (1968).Google Scholar
  373. 373.
    A. R. Rajwade, “Arithmetic on curves with complex multiplication by the Eisenstein integers,” Proc. Cambrisge Philos. Soc., 65(1):59–73 (1969).Google Scholar
  374. 374.
    S. S. Rangachari, “Abelian varieties attached to automorphic forms,” J. Math. Soc. Japan, 14(3):300–311 (1962).Google Scholar
  375. 375.
    G. Rauzy, “Points transcendants sur les variétiés de groupe,” Sémin. Bourbaki. Secret. Math., 16(3):276/01–276/08 (1963–1964).Google Scholar
  376. 376.
    M. Raynaud, “Caractéristique d'Euler-Poincaré d'un faisceau et cohomologie des variétés abéliennes,” Semin. Bourbaki. Secrét. math., 17(2):286-01–286-19 (1966); Dix exposés cohomol. schémas. Amsterdam-Paris (1968), pp. 12–30.Google Scholar
  377. 377.
    M. Raynaud, “Modeles de Néron,” C. r. Acad. Sci., AB262(6):A345-A347 (1966).Google Scholar
  378. 378.
    M. Raynaud, “Specialisation du foncteur de Picard,” C. r. Acad. sci., 264(22):A941-A943 (1967).Google Scholar
  379. 379.
    M. Raynaud, “Specialisation du foncteur de Picard. II. Critere numérique de représentabilité,” C. r. Acad. sci., 264(23):A1001-A1004 (1967).Google Scholar
  380. 380.
    D. Reich, “A p-adic fixed point formula,” Amer. J. Math., 51(3):835–850 (1969).Google Scholar
  381. 381.
    P. Ribenboim, “La conjecture d'Artin sur les equations diophantiennes,” Queen's Papers Pure and Appl. Math., No. 14, p. 167.(1968).Google Scholar
  382. 382.
    P. Roquette, “On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras,” Math. Ann., 150(5):411–439 (1963).Google Scholar
  383. 383.
    P. Roquette, “Splitting of algebras by function fields of one variable,” Nagoya Math. J., 27(2):625–642 (1966).Google Scholar
  384. 384.
    P. Roquette, “Analytische Theorie der p-adischen elliptischen Funktonen,” Sitzungsber. Berliner Math. Ges., 1967–1968, S. 1, 1969, 38.Google Scholar
  385. 385.
    C. Ryavec, “Cubic forms over algebraic number fields,” Proc. Cambridge Philos. Soc., 66(2):323–333 (1969).Google Scholar
  386. 386.
    P. Samuel, “La conjecture de Mordell pour les corps de fonctions,” Sémin. Bourbaki. Secrét. math., 1964–1965, 17(2):287/01–287/19 (1966).Google Scholar
  387. 387.
    P. Samuel, “Compléments a un article de Hans Grauert sur la conjecture de Mordell,” Publs math. Inst. hautes études scient., No. 29, 311–318 (1966).Google Scholar
  388. 388.
    P. Samuel, “A propos d'équations diophantiennes,” Bull. Assoc. professeurs math. enseign. public., 46(256):5–10 (1967).Google Scholar
  389. 389.
    P. Samuel, “Courbes algébriques,” Enseign. math., 13(4):305–311 (1968).Google Scholar
  390. 390.
    I. R. Shafarevich [Schafarewitsch], “Einige Anwendungen der Galoisschen Theorie auf Diophantische Gleichungen,” Schriftenr. Inst. Math. Dtsch. Akad. Wiss. Berlin, No. 13, 81–82 (1963).Google Scholar
  391. 391.
    I. R. Shafarevich [Schafarewitsch], “Lectures on minimal models and birational transformations of two dimensional schemes,” Tata Institute of Fundamental Research, Bombay (1966), p. 175.Google Scholar
  392. 392.
    S. Schanuel, “On heights in number fields,” Bull. Amer. Math. Soc., 70(2):262–263 (1964).Google Scholar
  393. 393.
    W. Schaflau, “Über die Brauer-Gruppe eines algebraischen Funktpnenkorpers in einer Variablen,” J. reine und angew. Math., 239-240(1):1–6 (1969).Google Scholar
  394. 394.
    W. Schmidt, “On heights of algebraic subspaces and diophantine approximations,” Ann. Math., 85(3):430–472 (1967).Google Scholar
  395. 395.
    B. Segre, “Intorno ad una congettura di Lang e Weil,” Atti Accad. naz. Lincei. Rend. Cl. sci. fis., mat. e natur., 34(4):337–339 (1963).Google Scholar
  396. 396.
    S. Sen abd J. Tate, “Ramification groups of local fields,” J. Indian Math. Soc., 1963, 27(3–4):197–202 (1964).Google Scholar
  397. 397.
    J.-P. Serre, “Endomorphismes complement continus des espaces de Banach p-adiques,” Publs. math. Inst. hautes études scient., 12:69–85 (1962).Google Scholar
  398. 398.
    J.-P. Serre, “Cohomologie galoisienne des groupes algébriques linéaries,” Colloq. théor. groupes algebr. Bruxelles, 1962, Louvain-Paris (1962), pp. 53–68.Google Scholar
  399. 399.
    J.-P. Serre, “Groupes analytiques p-adiques,” Sémin. Bourbaki. Secrét, math., 16(2):270/01–270/10 (1963–1964).Google Scholar
  400. 400.
    J.-P. Serre, “Exemples de variétés projectives conjuguées non homéormorphes,” C. r. acad sci., 258(17):4194–4196 (1964).Google Scholar
  401. 401.
    J.-P. Serre, “Sur les groupes de congruences des variétés abéliennes,” Izv. AN SSSR. Ser. Mat., 28(1):3–20 (1964).Google Scholar
  402. 402.
    J.-P. Serre, “Zeta and L functions,” Lect. Notes. Amer. Math. Soc. and Summer Inst. Algebr. Geometry, Woods Hole, Mass., 1964, S. 1, s. a., 1–13; Arithmet. Algebraic Geometry, Proc. Conf., Purdue Univ., 1963, New York (1965), pp. 82–92.Google Scholar
  403. 403.
    J.-P. Serre, “Cohomologie Galoisienne,” Lect. Notes Math., No. 5, p. 194 (1965).Google Scholar
  404. 404.
    J.-P. Serre, “Groupes de Liel-adiques attachés aux courbes elliptiques,” Colloq. internat. Centre nat. rech. scient., No. 143, 239–256 (1966).Google Scholar
  405. 405.
    J.-P. Serre, “Sur les groupes de Galois, attachés aux groupes p-divisibles,” Proc. Conf. Local Fields, Driebergen, 1966. Berlin-Heidelber-New York (1967), pp. 118–131.Google Scholar
  406. 406.
    J.-P. Serre, “Une interprétation des congruences relatives a la function τ de Ramanujan,” Sémin. théor. nombres Xelange-Pisot-Poitou. Fac. Sci. Paris, 1967–1968, 9(1):14/01–14/17 (1969).Google Scholar
  407. 407.
    J.-P. Serre, Abelianl-adic representations and elliptic curves,” New York, Benjamin (1968), 208 pp.Google Scholar
  408. 408.
    J.-P. Serre, “Facteurs locaux des fonctions zeta des vériétés algébriques (définitions et conjectures),” Sémin. Delange-Pisot-Poitou. Théor. nombres. Fac. sci. Paris, 11(2):19/01–19/15 (1969–1970.Google Scholar
  409. 409.
    J.-P. Serre and J. Tate, “Good reduction of Abelian varieties,” Ann. Math., 88(3):492–517 (1968).Google Scholar
  410. 410.
    S. S. Shatz, “Cohomology of artinian group schemes over local fields,” Ann. Math., 79(3):411–449 (1964).Google Scholar
  411. 411.
    S. S. Shatz, “Grothendieck topologies over complete local rings,” Bull. Amer. Math. Soc., 72(2):303–306 (1966).Google Scholar
  412. 412.
    S. S. Shatz, “The cohomological dimension of certain Grothendieck topologies,” Ann. Math., 83(3):572–595 (1966).Google Scholar
  413. 413.
    S. S. Shatz, “The cohomology of certain elliptic curves over local and quasi-local fields,” III. J. Math., 11(2):234–241 (1967).Google Scholar
  414. 414.
    S. S. Shatz, “Principal homogeneous spaces for finite group schemes,” Proc. Amer. Math. Soc., 22(3):678–680 (1969).Google Scholar
  415. 415.
    G. Shimura, “On the zeta-functions of the algebraic curves uniformized by certain automorphic functions,” J. Math. Soc. Japan, 13(3):275–331 (1961).Google Scholar
  416. 416.
    G. Shimura, “On the class-fields obtained by complex multiplication of Abelian varieties,” Osaka J. Math., 14(1):33–44 (1962).Google Scholar
  417. 417.
    G. Shimura, “On Dirichlet series and Abelian varieties attached to automorphic forms,” Ann. Math., 76(2):237–294 (1962).Google Scholar
  418. 418.
    G. Shimura, “On modular correspondences for Sp(n, Z) and their congruence relations,” Proc. Nat. Acad. Sci. USA, 49(6):824–828 (1963).Google Scholar
  419. 419.
    G. Shimura, “On purely transcendental fields of automorphic functions of several variables,” Osaka. J. Math., 1(1):1–14 (1964).Google Scholar
  420. 420.
    G. Shimura, “On the field of definition for afield of automorphic functions,” Ann. Math., 80(1):160–189 (1964).Google Scholar
  421. 421.
    G. Shimura, “The zeta-function of an algebraic variety and automorphic functions,” Lect. Notes. Amer. Math. Soc. and Summer Inst. Algebr. Geometry, Woods Hole, Mass. (1964), S. 1., s. a., 1–23.Google Scholar
  422. 422.
    G. Shimura, “Number fields and zeta-functions associated with discontinuous groups and algebraic varieties,” Proc. Internat. Congr. Mathematicians, 1966 [in Russian], “Mir,” Moscow (1968), pp. 290–299.Google Scholar
  423. 423.
    G. Shimura, “Number fields and zeta-functions associated with discontinuous groups and algebraic varieties,” in: Internat. Congr. Mathematicians. Report Abstracts [in Russian], Moscow (1966), pp. 100–107.Google Scholar
  424. 424.
    G. Shimura, “A reciprocity law in nonsolvable extensions,” J. reine und angew. Math., 221:209–220 (1966).Google Scholar
  425. 425.
    G. Shimura, “Moduli and fibre systems of Abelian varieties,” Ann. Math., 83(2):294–338 (1966).Google Scholar
  426. 426.
    G. Shimura, “Discontinuous groups and Abelian varieties,” Math. Ann., 168:171–199 (1967).Google Scholar
  427. 427.
    G. Shimura, “Construction of class fields and zeta-functions of algebraic curves,” Ann. Math., 85(1):58–159 (1967).Google Scholar
  428. 428.
    G. Shimura, “Algebraic varieties without deformation and the Chow variety,” J. Math. Soc. Japan, 20(1–2):336–341 (1968).Google Scholar
  429. 429.
    G. Shimura, “Automorphic functions and number theory,” Berlin, Springer (1968), p. 69.Google Scholar
  430. 430.
    G. Shimura and Y. Taniyama, “Complex multiplication of Abelian varieties and its applications to number theory,” S. 1., Math. Soc. Japan (1961).Google Scholar
  431. 431.
    K. Shiratani, “Über singuläre Invarianten elliptischer Funktionenkorper,” J. reine und angew. Math., 226:108–115 (1967).Google Scholar
  432. 432.
    K. Shiratani, “On certain formal Lie groups over p-adic integer rings,” Mem. Fac. Sci. Kyushu Univ. A22(1):31–42 (1968).Google Scholar
  433. 433.
    K. Shiratani, “Note on isogenies of one-parameter formal Lie groups over local integer rings,” Mem. Fac. Sci. Kyushu Univ., A23(2):156–158 (1969).Google Scholar
  434. 434.
    K. Shiratani, “On the Lubin-Tate reciprocity law,” J. Number Theory, 1(4):494–499 (1969).Google Scholar
  435. 435.
    T. Skolem, “A general remark concerning the study of rational points on algebraic curves,” Kgl. norske vid. selskabs forhandl., 36(1):3 (1963).Google Scholar
  436. 436.
    H. M. Stark, “The role of modular functions in a class-number problem,” J. Number Theory, 1(2):252–260 (1969).Google Scholar
  437. 437.
    N. M. Stephens, “Conjectures concerning elliptic curves,” Bull. Amer. Math. Soc., 73(1):160–163 (1967).Google Scholar
  438. 438.
    N. M. Stephens, “The diophantine equation X3+Y3= DZ3 and the conjectures of Birch and Swinnerton-Dyer,” J. reine und angew. Math., 231:121–162 (1968).Google Scholar
  439. 439.
    N. M. Stephens, “A corollary to a conjecture of Birch and Swinnerton-Dyer,” J. London Math. Soc., 43(1):146–148 (1968).Google Scholar
  440. 440.
    H. P. F. Swinnerton-Dyer, “The conjectures of Birch and Swinnerton-Dyer, and of Tate,” Proc. Conf. Local Fields, Driebergen, 1966. Berlin-Heidelberg-New York (1967), pp. 132–157.Google Scholar
  441. 441.
    H. P. F. Swinnerton-Dyer, “An application of computing to class field theory,” Algebr. Number Theory. London-New York, Acad. Press (1967), pp. 280–291.Google Scholar
  442. 442.
    H. P. F. Swinnerton-Dyer, “The zeta-function of a cubic surface over a finite field,” Proc. Cambridge Philos. Soc., 63(1):63(1):55–71 (1967).Google Scholar
  443. 443.
    T. Takahashi, “Galois cohomology of finitely generated modules,” Tohoku Math. J., 21(1):102–111 (1969).Google Scholar
  444. 444.
    J. Tate, “Duality theorems in Galois cohomology over number fields,” Proc. Internat. Congr. Math. Aug. 1962, Djursholm, Uppsala (1963), pp. 288–295.Google Scholar
  445. 445.
    J. Tate, “Algebraic cohomology classes,” Lect. Notes. Amer. Math. Soc. and Summer Inst. Algebr. Geometry, Woods Hole, Mass. 1964. S. 1., s. a., 1–25;Google Scholar
  446. 446.
    J. Tate, “The cohomology groups of tori in finite galois extensions of number fields,” Nagoya Math. J., 27(2):709–719 (1966).Google Scholar
  447. 447.
    J. Tate, “Endomorphisms of Abelian varieties over finite fields,” Invent. Math., 2(2):134–144 (1966).Google Scholar
  448. 448.
    J. Tate, “Multiplication complexe formelle dans les corps locaux,” Colloq. internat. Centre nat. rech. scient., No. 143, 257–258 (1966).Google Scholar
  449. 449.
    J. Tate, “p-divisible groups,” Proc. Conf. Local Fields, Driebergen, 1966. Berlin-Heidelberg-New York (1967), pp. 158–183.Google Scholar
  450. 450.
    J. Tate, “On the conjecture of Birch and Swinnerton-Dyer and a geometric analog,” Dix exposés cohomol. schémas. Amsterdam-Paris (1968), pp. 189–214.Google Scholar
  451. 451.
    G. Terjanian, “Un contre-exemple a une conjecture d'Artin,” C. r. Acad. sci., AB262(11):A612 (1966).Google Scholar
  452. 452.
    G. Terjanian, “Progrés récents dans 1'étude de la propriéte Ci des corps,” Sémin. Delange-Pisot-Poitou. Fac. sci. Paris, 1966–1967, 8(2):13/01–13/07 (1968).Google Scholar
  453. 453.
    A. I. Thaler, “A multiple-variable deformation theory for the zeta-function of a non-singular hypersurface,” Doct. diss. Johns Hopkins Univ. (1966), p. 57. Dissert. Abstrs. B29(8):2997 (1969).Google Scholar
  454. 454.
    U. Tiemmeier, “Unverzweigte galoissche p-Erweiterungen algebraischer Funktonenkorper mit endlichem Konstantenkorper,” Arch. Math., 20(6):590–596 (1969).Google Scholar
  455. 455.
    C. Traverso, “Sulla classificazione dei gruppi analitici commutativi di caratteristica positiva,” Ann. Scuola norm. super. Pisa Sci. fis. e mat., 23(3):481–507 (1969).Google Scholar
  456. 456.
    K. Uchida, “On Tate's duality theorems in Galois cohomology,” Tohoku Math. J., 21(1):92–101 (1969).Google Scholar
  457. 457.
    J. L. Verdier, “The Lefschetz fixed point formula in etale cohomology,” Proc. Conf. Local Fields, Driebergen, 1966. Berlin-Heidelberg-New York (1967), pp. 199–214.Google Scholar
  458. 458.
    W. Waterhouse, “A classification of almost full formal groups,” Proc. Amer. Math. Soc., 20(2):426–428 (1969).Google Scholar
  459. 459.
    W. Waterhouse, “Abelian varieties over finite fields,” Ann. sci. Ecole norm, supér, 1969, 2(4):521–560 (1970).Google Scholar
  460. 460.
    A. Weil, “Sur la théorie des formes quadratiques,” Colloq. théor. groupes algébr. Bruxelles, 1962. Louvain-Paris (1962), pp. 9–22.Google Scholar
  461. 461.
    A. Weil, “Sur la formule de Siegel dans théorie des groupes classiques,” Acta math., 113(1-2):1–87 (1965).Google Scholar
  462. 462.
    A. Weil, “Über die Bestimmung Dirichletscher Reihen durch Funktonalgleichungen,” Math. Ann., 168:149–156 (1967).Google Scholar
  463. 463.
    A. Weil, “Zeta-functions and Melin transforms,” Algebr. Geom. London (1969), pp. 409–426.Google Scholar
  464. 464.
    A. Weil, “On the analogue of the modular group in characteristic p,” Functional Analysis and Relat. Fields. Berlin et al. (1970), pp. 211–223.Google Scholar
  465. 465.
    C. Weisman, “On the connected identity component of the Adele-class group of an algebraic torus,” Proc. Amer. Math. Soc., 21(1):155–160 (1969).Google Scholar
  466. 466.
    T. Yamada, “On the Jacobian varieties of Davenport-Hasse curves,” Proc. Japan Acad., 43(6):407–411 (1967).Google Scholar
  467. 467.
    T. Yamada, “On the Davenport-Hasse curves,” J. Math. Soc. Japan, 20(1–2):403–410 (1968).Google Scholar
  468. 468.
    H. Yanagihara, “Reduction of group varieties and transformation spaces,” J. Sci. Hiroshima Univ. 1963, Ser. A, Div. 1, 27(1):35–49 (1963).Google Scholar
  469. 469.
    H. Yanagihara, “Reduction of models over a discrete valuation ring,” J. Math. Kyoto Univ., 2(2):123–156 (1963).Google Scholar
  470. 470.
    H. Yanagihara, “Corrections and supplement to the paper ‘Reduction of models over a discrete valuation ring,’” J. Math. Kyoto Univ., 3(3):363–368 (1964).Google Scholar

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© Consultants Bureau 1973

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  • A. N. Parshin

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