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Inventiones mathematicae

, Volume 94, Issue 3, pp 529–573 | Cite as

On ordinary λ-adic representations associated to modular forms

  • A. Wiles
Article

Keywords

Modular Form 
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References

  1. [A] Arthur, J.: The Selberg trace formula for groups ofF-rank one. Ann. Math.100, 326–385 (1974)Google Scholar
  2. [BL] Brylinski, J.L. Labesse, J.P.: Cohomologies d'intersection et fonctionsL de certaines variétes de Shimura. Ann. Sci. Ec. Norm. Super., IV. Ser.17, 361–412 (1984)Google Scholar
  3. [Car] Carayol, H.: Sur les représentationsP-adiques associées aux formes modulaires de Hilbert. Ann. Sci. Ec. Norm. Super., IV. Ser.19, 409–468 (1986)Google Scholar
  4. [Cas] Casselman, W.: An assortment of results on representations ofGL 2(k). In: Modular functions of one variable, II. (Lecture Notes in Mathematics, Vol. 349, pp. 1–54). Berlin-Heidelberg-New York: Springer 1973Google Scholar
  5. [De] Demazure, D.: Lectures onp-divisible groups. (Lecture Notes in Mathematics, Vol. 302). Berlin-Heidelberg-New York: Springer 1972Google Scholar
  6. [DR] Deligne, P., Ribet, K.: Values of abelianL-functions at negative integers over totally real fields. Invent. Math.59, 227–286 (1980)Google Scholar
  7. [DS] Deligne, P., Serre, J.-P.: Formes modulaires de poids 1. Ann. Sci. Ec. Norm. Super., IV. Ser.7, 507–530 (1974)Google Scholar
  8. [G] Greenberg, R.: Onp-adic ArtinL-functions. Nagoya Math. J.89, 77–87 (1983)Google Scholar
  9. [HLR] Harder, G., Langlands, R.P., Rapoport, M.: Algebraische Zyklen auf Hilbert-Blumenthal-Flächen. J. Reine Angew. Math.366, 53–120 (1986)Google Scholar
  10. [Hi1] Hida, H.: On congruence divisors of cusp forms as factors of the special values of their zeta functions. Invent. Math.64, 221–262 (1981)Google Scholar
  11. [Hi2] Hida, H.: Galois representations intoGL 2(Z p[[x]]) attached to ordinary cusp forms. Invent. Math.85, 546–613 (1986)Google Scholar
  12. [Hi3] Hida, H.: On abelian varieties with complex multiplication as factors of the jacobians of Shimura curves. Am. J. Math.103, 727–776 (1981)Google Scholar
  13. [Hi4] Hida, H.: Onp-adic Hecke algebras forGL 2 over totally real fields. PreprintGoogle Scholar
  14. [Hi5] Hida, H.: Iwasawa modules attached to congruences of cusp forms. Ann. Sci. Ec. Norm. Supper., IV. Ser.19, 231–273 (1986)Google Scholar
  15. [JL] Jacquet, H., Langlands, R.P.: Automorphic forms onGL.(2). (Lecture Notes in Mathematics, Vol. 114). Berlin-Heidelberg-New York: Springer 1970Google Scholar
  16. [JS] Jacquet, H., Shalika, J.: On Euler products and the classification of automorphic forms I and II. Am. J. Math.103, 499–558, 777–815 (1981)Google Scholar
  17. [KL] Katz, N.M., Laumon, G.: Transformation de Fourier et majoration de sommes exponentielles. Publ. Math., Inst. Hautes Etud. Sci.62, 145–202 (1986)Google Scholar
  18. [MS] Matzushima, Y., Shimura, G.: On the cohomolgy of groups attached to certain vector valued forms on the product of upper half planes. Ann. Math.78, 417–449 (1963)Google Scholar
  19. [MW1] Mazur, B., Wiles, A.: Onp-adic analytic families of Galois represenations. Comp. Mech.59, 231–264 (1986)Google Scholar
  20. [MW2] Mazur, B., Wiles, A.: Class fields of abelian extensions ofQ. Invent. Math.76, 179–330 (1984)Google Scholar
  21. [Ra] Ramakrishnan, D.: Arithmetic of Hilbert-Blumenthal surfaces. Number theory, Proceedings of the Montreal Conference, CMS conference proceedings7, 285–370 (1987)Google Scholar
  22. [Ri] Ribet, K.: Congruence relations between modular forms, Proc. International Congress of Mathematicians (1983), pp. 503–514Google Scholar
  23. [RT] Rogawski, J.D., Tunnell, J.B.: On ArtinL-functions associated to Hilbert modular forms of weight one. Invent. Math.74, 1–42 (1983)Google Scholar
  24. [Se1] Serre, J.-P.: Abelianl-adic representations and elliptic curves. New York: W.A. Benjamin Inc. 1968Google Scholar
  25. [Se2] Serre, J.-P.: Quelques applications de théoréme de densité de Chebotarev. Publ. Math., Inst. Hautes Etud. Sci.54, 123–202 (1981)Google Scholar
  26. [Sh 1] Shimura, G.: The special values of the zeta functions associated with Hilbert modular forms. Duke Math. J.45, 637–679 (1978)Google Scholar
  27. [Sh 2] Shimura, G.: The special values of the zeta functions associated with cusp forms. Commun. Pure Appl. Math.29, 783–804 (1976)Google Scholar
  28. [Sh3] Shimura, G.: Anl-adic method in the theory of automorphic forms. Unpublished (1968)Google Scholar
  29. [Si] Siegel, C.: Über die Fouriersche Koeffizienten von Modulformen. Gött. Nach.3, 15–56 (1970)Google Scholar
  30. [T] Tate, J.: Number theoretic background. In: Automorphic forms, representations andL-functions, Proc. Symp. Pure Math., 33, (part 2) 3–26 (1979)Google Scholar
  31. [W1] Wiles, A.: Onp-adic representations for totally real fields. Ann. Math.123, 407–456 (1986)Google Scholar
  32. [W2] Wiles, A.: The Iwawawa conjecture for totally real fields. (Submitted to Ann. Math.)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • A. Wiles
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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