Journal of Soviet Mathematics

, Volume 30, Issue 2, pp 2036–2070 | Cite as

Higher regulators and values of L-functions

  • A. A. Beilinson


In the work conjectures are formulated regarding the value of L-functions of motives and some computations are presented corroborating them.


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Literature cited

  1. 1.
    S. Yu. Arakelov, “Theory of intersections of divisors on an arithmetic surface,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 6, 1179–1192 (1974).Google Scholar
  2. 2.
    M. F. Atiyah, K-Theory, W. A. Benjamin (1967).Google Scholar
  3. 3.
    A. A. Beilinson, “Higher regulators and values of the L-functions of curves,” Funkts. Anal. Prilozhen.,14, No. 2, 46–47 (1980).Google Scholar
  4. 4.
    A. Weil, Elliptic Functions According to Eisenstein and Kronecker, Springer-Verlag (1976).Google Scholar
  5. 5.
    H. Jacquet and R. P. Langlands, Automorphic Forms on GL(2), Springer-Verlag (1970).Google Scholar
  6. 6.
    Yu. I. Manin, “Correspondences, motifs, and monoidal transformations,” Mat. Sb.,77, No. 4, 475–507 (1968).Google Scholar
  7. 7.
    A. A. Suslin, “Algebraic K-theory,” Itogi Nauki i Tekh. VINITI. Algebra. Topologiya. Geometriya, Vol. 20 (1982), pp. 71–152.Google Scholar
  8. 8.
    S. Bloch, “Applications of the dilogarithm function in algebraic K-theory and algebraic geometry,” Proc. Int. Symp. on Alg. Geometry, Kyoto (1977), pp. 103–114.Google Scholar
  9. 9.
    S. Bloch, “Higher regulators, algebraic K-theory, and zeta-functions of elliptic curves,” Irvine Univ. Preprint (1978).Google Scholar
  10. 10.
    S. Bloch, “Lectures on algebraic cycles,” Duke Univ. Math. Series, No. 4 (1980).Google Scholar
  11. 11.
    S. Bloch, “The dilogarithm and extensions of Lie algebras,” Lect. Notes Math.,B54, 1–23 (1981).Google Scholar
  12. 12.
    A. Borel, “Stable and real cohomology of arithmetic groups,” Ann. Sci. ENS,7, 235–272 (1974).Google Scholar
  13. 13.
    A. Borel, “Cohomologie de SLn et valeurs de fonctions zeta aux points entiers,” Ann. Scu. Norm. Super. Pisa Cl. Sci.,4, No. 4, 613–636 (1977).Google Scholar
  14. 14.
    A. K. Bousfield and D. M. Kan, “Homotopy limits, completions and localizations,” Lect. Notes Math.,304 (1972).Google Scholar
  15. 15.
    P. Deligne, “Theorie de Hodge. II,” Publ. Math. Inst. Hautes Etudes Scient.,40, 5–58 (1971).Google Scholar
  16. 16.
    P. Deligne, “Theorie de Hodge. III,” Publ. Math. Inst. Hautes Etudes Scient.,44, 5–77 (1974).Google Scholar
  17. 17.
    P. Deligne, “Les constantes des equations fonctionelles des fonctions L,” Lect. Notes Math.,349, 501–597 (1973).Google Scholar
  18. 18.
    P. Deligne, “Valeurs de fonctions L et periodes d'integrales,” Automorphic Forms, Representations, and L-Functions, Proc. Symp. Pure Math. Am. Math. Soc., Corvallis, Ore. (1977), Part 2, Providence, R.I. (1979), pp. 313–346.Google Scholar
  19. 19.
    P. Deligne, “Le symbole modere,” Manuscript (1979).Google Scholar
  20. 20.
    P. Deligne and M. Rapoport, “Les schemas de modules de courbes elliptiques,” Lect. Notes Math.,349, 143–316 (1973).Google Scholar
  21. 21.
    J. Dupont, “Simplicial de Rham cohomology and characteristic classes of flat bundles,” Topology,15, No. 3, 233–245 (1976).CrossRefGoogle Scholar
  22. 22.
    H. Gillet, “Riemann-Roch theorems for higher algebraic K-theory,” Adv. Math.,40, 203–289 (1981).CrossRefGoogle Scholar
  23. 23.
    H. Gillet, “Comparison of K-theory spectral sequences with applications,” Lect. Notes Math., No. 854, 141–167 (1981).Google Scholar
  24. 24.
    B. Gross, “Higher regulators and values of Artin's L-functions,” Preprint (1979).Google Scholar
  25. 25.
    H. Jacquet, “Automorphic forms on GL(2),” Lect. Notes Math., No. 78 (1971).Google Scholar
  26. 26.
    Ch. Kratzer, “λ-structure en K-theorie algebrique,” Comment. Math. Helv.,55, No. 2, 233–254 (1980).Google Scholar
  27. 27.
    J.-L. Loday, “Symboles en K-theorie algebrique superiore,” C. R. Acad. Sci.,292, 863–867 (1981).Google Scholar
  28. 28.
    D. Quillen, “Higher algebraic K-theory. I,” Lect. Notes Math., No. 341 (1973).Google Scholar
  29. 29.
    B. Saint-Donat, “Technique de descent cohomologique,” Lect. Notes Math.,270, 83–162 (1972).Google Scholar
  30. 30.
    Ch. Soulé, “Operations en K-theorie algebrique,” Preprint (1980).Google Scholar
  31. 31.
    A. Suslin, “Homology of GLn, characteristic classes, and Milnor's K-theory,” Preprint, LOMI (1982).Google Scholar
  32. 32.
    J. Tate, “Algebraic cycles and poles of zeta functions,” Arithmetical Algebraic Geometry, New York (1965), pp. 93–100.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • A. A. Beilinson

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