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Inventiones mathematicae

, Volume 96, Issue 1, pp 1–69 | Cite as

Higher regulators and HeckeL-series of imaginary quadratic fields I

  • Christopher Deninger
Article

Keywords

High Regulator Quadratic Field Imaginary Quadratic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [A] Adams, J.F.: On the groupsJ(X) II. Topology3, 137–171 (1965)Google Scholar
  2. [Be1] Beilinson, A.A.: Higher regulators and values ofL-functions of curves. Funct. Anal. Appl.14, 116–118 (1980)Google Scholar
  3. [Be2] Beilinson, A.A.: Higher regulators and values ofL-functions. J. Sov. Math.30, 2036–2070 (1985)Google Scholar
  4. [Be3] Beilinson, A.A.: Higher regulators of modular curves. Contemp. Math.55 (I) 1–34 (1986)Google Scholar
  5. [Be4] Beilinson, A.A.: Notes on absolute Hodge cohomology. Contemp. Math.55, (I) 35–68 (1986)Google Scholar
  6. [Bl1] Bloch, S.: AlgebraicK-theory and zeta functions of elliptic curves. Proc. Int. Cong. of Math., Helsinki, pp. 511–515 (1978)Google Scholar
  7. [Bl2] Bloch, S.: Lectures on algebraic cycles. Duke Univ. Math. series, lectures 8, 9 (1981)Google Scholar
  8. [Bl3] Bloch, S.: Algebraic cycles and higherK-theory. Adv. Math.61, 267–304 (1986)Google Scholar
  9. [Bl4] Bloch, S.: Algebraic cycles and the Beilinson conjectures. Contemp. Math.58, (I) 65–79 (1986)Google Scholar
  10. [Bl-G] Bloch, S., Grayson, D.:K 2 andL-functions of elliptic curves. Computer calculations. Contemp. Math.55, (I) 79–88 (1986)Google Scholar
  11. [Bo] Borel, A.: Stable real cohomology of arithmetic groups. Ann. Sci. Ec. Norm. Super., IV. Ser.7, 235–272 (1974)Google Scholar
  12. [C-Sh] Coleman, R., de Shalit, E.:p-adic regulators on curves and special values ofp-adicL-functions. Invent. Math.93, 239–266 (1988)Google Scholar
  13. [Co] Colmez, P.: Valeurs spéciales de fonctionsL attachées à des charactères de Hecke de typeA 0 d'une extension d'un corps quadratique imaginaire. ThèseGoogle Scholar
  14. [D1] Deligne, P.: Valeurs de fonctionsL et périodes d'intégrales. Proc. Symp. Pure Math.33, (2) 313–346 (1979)Google Scholar
  15. [D2] Deligne, P.: Théorie de Hodge II. Publ. Math., Inst. Hautes Etud. Sci.40, 5–57 (1972)Google Scholar
  16. [De-W] Deninger, C., Wingberg, K.: On the Beilinson conjectures for elliptic curves with complex multiplication. In: Rapoport, M., Schappacher, N., Schneider, P. (eds.) Beilinson's conjectures on special values ofL-functions. (Perspectives in Math., Vol. 4.) Boston-New York: Academic Press 1988Google Scholar
  17. [De] Deninger, C.: Higher regulators of elliptic curves with complex multiplication. To appear in: Séminaire de Théorie de nombres, edited by Ch. Goldstein, Paris 1986/87Google Scholar
  18. [E-V] Esnault, H., Viehweg, E.: Deligne-Beilinson cohomology. In: Rapoport, M., Schappacher, N., Schneider, P. (eds.) Beilinson's conjectures on special values ofL-functions. (Perspectives in Math., Vol. 4.) Boston-New York: Academic Press 1988Google Scholar
  19. [F] Fujiki, A.: Duality of mixed Hodge structures of algebraic varieties. Publ. Res. Inst. Math. Sci.16, 635–667 (1980)Google Scholar
  20. [G-Sch] Goldstein, Ch., Schappacher, N.: Séries d'Eisenstein et fonctionsL de courbes elliptiques à multiplication complexe. J. Reine Angew. Math.327, 184–218 (1981)Google Scholar
  21. [Gr] Gross, B.: Arithmetic on elliptic curves with complex multiplication. (Lect. Notes Math., Vol. 776). Berlin-Heidelberg-New York: Springer 1980Google Scholar
  22. [G, SGA1] Grothendieck, A., Raynaud, M.: Revêtements étales et groupe fondamental, SGA 1. (Lect. Notes Math., Vol. 224.) Berlin-Heidelberg-New York: Springer 1971Google Scholar
  23. [J] Jannsen, U.: Deligne homology, Hodge 68-1, and motives. In: Rapoport, M., Schappacher, N., Schneider, P. (eds.) Beilinson's conjectures on special values ofL-functions. (Perspectives in Math., Vol. 4.) Boston-New York: Academic Press 1988Google Scholar
  24. [K] Kato, K.: A Hasse principle for two dimensional global fields. J. Reine Angew. Math.366, 142–181 (1986)Google Scholar
  25. [L] Lang, S.: Elliptic functions. New York: Addison-Wesley (1973)Google Scholar
  26. [Ma] Manin, Y.I.: Correspondences, motives and monoidal transformations. Mat. Sbor.77, 475–507 (1970) (AMS Transl.)Google Scholar
  27. [Mi] Milne, J.S.: On the arithmetic of abelian varieties. Invent. Math.17, 177–190 (1972)Google Scholar
  28. [Ro] Rohrlich, D.: Elliptic curves and values ofL-functions. In: Kisilevsky, H., Labute, J. (eds) Proc. of the CMS summer school on algebraic number theory. Montreal (1985)Google Scholar
  29. [Sch] Schneider, P.: Introduction to the Beilinson conjectures. In: Rapoport, M., Schappacher, N., Schneider, P. (eds.) Beilinson's conjectures on special values ofL-functions. (Perspectives in Math., Vol. 4.) Boston-New York: Academic Press 1988Google Scholar
  30. [S-T] Serre, J.P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492–517 (1968)Google Scholar
  31. [Sh] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Princeton: Princeton University Press 1971Google Scholar
  32. [So1] Soulé, Ch.: Opérations enK-théorie algébrique. Can. J. Math.37, 488–550 (1985)Google Scholar
  33. [So2] Soulé, Ch.: Régulateurs. Séminaire Bourbaki 37 ème année no 644 (1984/85)Google Scholar
  34. [So3] Soulé, Ch.:p-adicK-theory of elliptic curves. Duke Math. J.54, 249–269 (1987)Google Scholar
  35. [Sp] Spivak, M.: Differential geometry I. Publish or Perish (1970)Google Scholar
  36. [Ta] Tamme, G.: The theorem of Riemann-Roch. In: Rapoport, M., Schappacher N., Schneider, P. (eds.) Beilinson's conjectures on special values ofL-functions. (Perspectives in Math., Vol. 4.) Boston-New York: Academic Press 1988Google Scholar
  37. [T] Tate, J.: On Fourier analysis in number fields and Hecke's zeta function. In: Cassels, J.W.S., Fröhlich, A. (eds.) (Algebraic Number Theory). Washington D.C.: Thompsen Book Comp. Inc. 1967Google Scholar
  38. [W1] Weil, A.: Variétés Abéliennes et Courbes Algébriques. Paris: Hermann 1948Google Scholar
  39. [W2] Weil, A.: Elliptic functions according to Eisenstein and Kronecker, Berlin-Heidelberg-New York: Springer 1976Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Christopher Deninger
    • 1
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgFederal Republic of Germany

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