Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I

  • Kazuya Kato
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Part of the Lecture Notes in Mathematics book series (LNM, volume 1553)

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Bibliography

  1. [Be1]
    Beilinson, A., Higher regulators and values of L-functions, J. Soviet Math. 30 (1985) 2036–2070.CrossRefMATHGoogle Scholar
  2. [Be2]
    Beilinson, A., Polylogarithm and cyclotomic elements, preprint.Google Scholar
  3. [Bl]
    Bloch, S., Lectures on algebraic cycles, Duke Univ. Math. Series (1980).Google Scholar
  4. [BK]
    Bloch, S. and Kato, K., L-functions and Tamagawa numbers motives, in The Grothendieck Festscherift, Vol. 1 (1980) 334–400.MATHGoogle Scholar
  5. [Bo]
    Borel, A., Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235–272.MathSciNetMATHGoogle Scholar
  6. [CP]
    Coates, J. and Perrin-Riou, B., On p-adic L-functions attached to motives over Q, in Advanced Studies in Pure Math. 17 (1989) 23–54.MathSciNetMATHGoogle Scholar
  7. [CW]
    Coates J. and Wiles, A., On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977) 223–251.MathSciNetCrossRefMATHGoogle Scholar
  8. [Co]
    Coleman, R., Division values in local fields, Inv. Math. 53 (1979) 91–116.MathSciNetCrossRefMATHGoogle Scholar
  9. [Da]
    Damerell, R. M., L-functions of elliptic curves with complex multiplication, I. Acta Arith. 17 (1970) 287–301, II, ibid. 19 (1971) 311–317.MathSciNetMATHGoogle Scholar
  10. [De1]
    Deligne, P., Théorie de Hodge II, Publ. Math. IHES 40 (1972) 5–57.CrossRefMATHGoogle Scholar
  11. [De2]
    Deligne, P., Théorème de finitude en cohomologie l-adique, in Lecture Notes in Math. 569 (SAG 4½), Springer (1977) 233–261.MathSciNetCrossRefMATHGoogle Scholar
  12. [De3]
    Valeurs de fonctions L et périodes d'intégrales, Proc. Symp. Pure Math., vol. 33, Part 2, AMS (1979) 313–349.Google Scholar
  13. [De4]
    Deligne, P., La conjecture de Weil II, Publ. Math. IHES 52 (1981).Google Scholar
  14. [De5]
    Deligne, P., Le groupe fondamental de la droite projective moins trois points, in Galois groups over Q. Springer (1989) 79–298.Google Scholar
  15. [dS1]
    de Shalit, E., The explicit reciprocity law in local class field theory, Duke Math. J. (1986) 163–176.Google Scholar
  16. [dS2]
    de Shalit, E., Iwasawa theory of elliptic curves with complex multiplication, Academic Press (1987).Google Scholar
  17. [dS3]
    de Shalit, E., The explicit reciprocity law of Bloch and Kato, preprint.Google Scholar
  18. [Fa]
    Faltings, G., Crystalline cohomology and p-adic Galois representations, in Algebraic Analysis, Geometry, and Number Theory, Johns Hopkins Univ. (1989) 25–80.Google Scholar
  19. [Fo1]
    Fontaine, J.-M., Sur certains types de représentations p-adiques du groupe de Galois d'un corps local: construction d'un anneau de Barsotti-Tate, Ann. of Math. 115 (1982) 547–608.MathSciNetCrossRefGoogle Scholar
  20. [Fo2]
    Fontaine, J.-M., Formes différentielles et modules de Tate des variétés abeliennes sur les corps locaux, Invent. Math. 65 (1982) 379–409.MathSciNetCrossRefMATHGoogle Scholar
  21. [Fo3]
    Fontaine, J.-M., Cohomologie crystalline et représentations p-adiques, in Lecture Notes in Math. 1016, Springer (1983) 86–108.Google Scholar
  22. [FM]
    Fontaine, J.-M. and Messing, W., p-adic periods and p-adic étale cohomology, Contemporary Math. 67 (1987) 179–207.MathSciNetCrossRefMATHGoogle Scholar
  23. [FP1]
    Fontaine, J.-M. and Perrin-Riou, B., Autour des conjectures de Bloch et Kato, I. C. R. Acad. Sci. Paris, t. 313, Série I (1991) 189–196, II, ibid., 349–356, III, ibid., 421–428.MathSciNetMATHGoogle Scholar
  24. [FP2]
    Fontaine, J.-M. and Perrin-Riou, B., Autour des conjectures de Bloch et Kato, cohomologie galoisienne et valeurs de fonctions L, preprint.Google Scholar
  25. [Gr]
    Grothendieck, A., Formule de Lefschetz et rationalité des fonctions L, in Sém. Bourbaki, vol. 1965/66, Benjamin (1966) exposé 306Google Scholar
  26. [11]
    Illusie, L., Cohomologie de de Rham et cohomologie étale p-adique (Sém. Bourbaki exposé 726), in Astérisque (1990) 325–374.Google Scholar
  27. [Ja]
    Jannsen, U., On the l-adic cohomology of varieties over number fields and its Galois cohomology, in Galois groups over Q, Springer (1989) 315–360.Google Scholar
  28. [Ka1]
    Kato, K., The explicit reciprocity law and the cohomology of Fontaine-Messing, Bull. Soc. Math. France 119 (1991) 397–441.MathSciNetMATHGoogle Scholar
  29. [Ka2]
    Kato, K., Iwasawa theory and p-adic Hodge theory, preprint.Google Scholar
  30. [Ka3]
    Kato, K., in preparation.Google Scholar
  31. [Ki]
    Kinoshita, J., The twilight-crane (1949). (A drama basing on a Japanese legend.)Google Scholar
  32. [KM]
    Knudsen, F. and Mumford, D., The projectivity of the moduli space of stable curves I, Math. Scand. 39, 1 (1976) 19–55.MathSciNetMATHGoogle Scholar
  33. [Ko]
    Kolyvagin, V. A., Euler systems, The Grothendieck Festschrift, vol. 2, Birkhaüser (1990) 435–483.MathSciNetGoogle Scholar
  34. [Ma]
    Mazur, B., Notes on the étale cohomology of number fields, Ann. Sci. Ec. Norm. Sup. 6 (1973) 521–556.MathSciNetMATHGoogle Scholar
  35. [MW]
    Mazur, B and Wiles, A., Class fields of abelian extensions of Q, Invent. Math. 76 (1984) 179–330.MathSciNetCrossRefMATHGoogle Scholar
  36. [Mi]
    Miyazawa K. (a Japanese poet), A night on the galaxy train (written around 1924).Google Scholar
  37. [Qu]
    Quillen, D., Higher algebraic K-theory, I., in Lecture Notes in Math. 341, Springer (1973) 85–147.Google Scholar
  38. [Ra]
    Rapoport, M., Schappacher, N. and Schneider, P. (ed.), Beilinson's conjectures on special values of L-functions, Academic Press (1988).Google Scholar
  39. [Ru]
    Rubin, K., The "main conjectures" of Iwasawa theory for imaginary quadratic fields, Invent. math. 103 (1991) 25–68.MathSciNetCrossRefMATHGoogle Scholar
  40. [Se]
    Serre, J.-P., Cohomologie Galoisienne, Lecture Notes in Math. 5, Springer (1965).Google Scholar
  41. [So1]
    Soulé, C., K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979) 251–295.MathSciNetCrossRefMATHGoogle Scholar
  42. [So2]
    Soulé, C., On higher p-adic regulators, in Lecture Notes in Math. 854, Springer (1981) 371–401.Google Scholar
  43. [So3]
    Soulé, C., The rank of étale cohomology of varieties over p-adic or number fields, Comp. Math. 53 (1984) 113–131.MATHGoogle Scholar
  44. [So4]
    Soulé, C., p-adic K-theory of elliptic curves, Duke Math. J. 54 (1987) 249–269.MathSciNetCrossRefMATHGoogle Scholar
  45. [Ta1]
    Tate, J., On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, in Sém. Bourbaki, vol. 1965/66, Benjamin (1966) exposé 306.Google Scholar
  46. [Ta2]
    Tate, J., p-divisible groups, Proceedings of a conference on local fields, Driebergen, 1966, Springer (1967) 158–183.Google Scholar
  47. [Wa]
    Washington, L. C., Introduction to cyclotomic fields, Springer (1982).Google Scholar
  48. [We1]
    Weil, A., Elliptic functions according to Eisenstein and Kronecker, Springer (1976).Google Scholar
  49. [We2]
    Weil, A., Number theory: An approach through history; From Hammurapi to Legendre, Birkhäuser (1983).Google Scholar
  50. [Wi1]
    Wiles, A., Higher explicit reciprocity laws, Ann. Math. 107 (1978) 235–254.MathSciNetCrossRefMATHGoogle Scholar
  51. [Wi2]
    Wiles, A., The Iwasawa conjecture for totally real fields, Ann. of Math. 131 (1990) 493–540.MathSciNetCrossRefMATHGoogle Scholar
  52. [Wo]
    Wolfgang, K. S., λ-rings and Adams operators in algebraic K-theory, included in [Ra], 93–102.Google Scholar
  53. [SGA4]
    Artin, M. and Grothendieck, and Verdier, J. L., Théorie des topos et cohomologie étale des schémas, Lecture Notes in Math. 269, 270, 305, Springer (1972/73).Google Scholar

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  • Kazuya Kato

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