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The weight in Serre's conjectures on modular forms

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References

  1. Ash, A., Stevens, G.: Modular forms in characteristicl and special values of theirL-functions. Duke Math. J.53, No. 3 (1986)

  2. Boston, N., Lenstra, H.W., Ribet, K.A.: Quotients of group rings arising from two-dimensional representations. C.R. Acad. Sci. Paris, Sér.I 312, 323–328 (1991)

    Google Scholar 

  3. Carayol, H.: Sur les représentationsl-adiques associées aux formes modulaires de Hilbert. Ann. Sci. Ec. Norm. Super., IV. Sér.19, 409–468 (1986)

    Google Scholar 

  4. Coleman, R.F.: Ap-adic Shimura isomorphism andp-adic periods of modular forms. (Preprint)

  5. Coleman, R.F., Voloch, J.F.: Companion forms and Kodaira-Spencer theory (to appear)

  6. Cornell, G., Silverman, J.H.: Arithmetic geometry. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  7. Deligne, P., Mumford, D.: The irreducibility of the space of curves of given genus. Publ. Math., Inst. Hautes Etud. Sci.36, 75–125 (1969)

    Google Scholar 

  8. Deligne, P., Rapoport, M.: Les schémas de modules des courbes elliptiques. In: Deligne, P., Kuyk, W. (eds.) Modular Functions of One Variable II. (Lect. Notes Math., vol. 349, pp. 143–316) Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  9. Deligne, P., Serre, J.-P.: Formes modulaires de poids 1. Ann. Sci. Ec. Norm. Super., IV. Sér.7, 507–530 (1974)

    Google Scholar 

  10. Gross, B.H.: A tameness criterion for Galois representations associated to modular forms (mod p). Duke Math. J.61, No. 2, (1990)

  11. Jordan, B., Livné, R.: Conjecture “epsilon” for weightk>2. Bull. Am. Math. Soc.21, 51–56 (1989)

    Google Scholar 

  12. Grothendieck, A.: Séminaire de géométrie algébrique. (Lect. Notes Math., vols. 151, 152, 153, 224, 225, 269, 270, 288, 305, 340, 589) Berlin Heidelberg New York: Springer 1970–1977

    Google Scholar 

  13. Jochnowitz, N.: The local components of the Hecke algebra modl. Trans. Am. Math. Soc.270, 253–267 (1982)

    Google Scholar 

  14. Katz, N.M.:p-adic properties of modular schemes and modular forms. In: Kuyk, W., Serre J.-P. (eds.) Modular Functions of One Variable III. (Lect. Notes Math., vol. 350, pp. 69–190) Berlin Heidelberg New York: Springer 1973

    Google Scholar 

  15. Katz, N.M.: A result on modular forms in characteristicp. In: Serre, J.-P., Zagier, D.B. (eds.) Modular Functions of One Variable V. (Lect. Notes Math., vol. 601, pp. 53–61) Berlin Heidelberg New York: Springer 1976

    Google Scholar 

  16. Katz, N.M., Mazur, B.: Arithmetic moduli of elliptic curves. (Ann. Math. Stud., vol. 108) Princeton: Princeton University Press 1985

    Google Scholar 

  17. Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math., Inst. Hautes Etud. Sci. 47 (1977)

  18. Mazur, B., Ribet, K.A.: Two-dimensional representations in the arithmetic of modular curves Astérisque (to appear)

  19. Oda, T.: The first De Rham cohomology group and Dieudonné modules. Ann. Sci. Ec. Norm. Super., IV. Sér.2, 63–135 (1969)

    Google Scholar 

  20. Raynaud, M.: Spécialisation du foncteur de Picard. Publ. Math. Inst. Hautes Etud. Sci. 38 (1970)

  21. Raynaud, M.: Schémas en groupes de type (p,...,p). Bull. Soc. Math. Fr.102, 241–280 (1974)

    Google Scholar 

  22. Ribet, K.A.: On modular representations of Gal (Q/ℚ) arising from modular forms. Invent. Math.100, 431–476 (1990)

    Google Scholar 

  23. Robert, G.: Congruences entres séries d'Eisenstein, dans le cas supersingulier. Invent. Math.61, 103–158 (1980)

    Google Scholar 

  24. Serre, J.-P.: Une interprétation des congruences relatives à la fonction τ de Ramanujan. Séminaire Delange-Pisot-Poitou 1967/68, 14, Oeuvres 80

  25. Serre, J.-P.: Valeurs propres des opérateurs de Hecke modulol. Journées arithmétiques Bordeaux. Astérisque 24–25, 109–117 (1975), Oeuvres 104

    Google Scholar 

  26. Serre, J.-P., Sur les représentations de degré 2 de Gal (594-1). Duke Math. J. 54, No. 1, (1987)

  27. Serre, J.-P., Résumé des cours au Collège de France, 1987–1988

  28. Szpiro, L.: Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell. Astérisque 127 (1985)

  29. Tate, J.: “p-divisible groups.” In: Proceedings of a conference on local fields at Driebergen, pp. 158–184. Berlin Heidelberg New York: Springer 1967

    Google Scholar 

  30. Ulmer, D.L.:L-functions of universal curves over Igusa curves. Am. J. Math.112, 687–712 (1990)

    Google Scholar 

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Oblatum 29-IV-1991 & 23-III-1992

Supported by the Netherlands Organisation for Scientific Research (NWO)

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Edixhoven, B. The weight in Serre's conjectures on modular forms. Invent Math 109, 563–594 (1992). https://doi.org/10.1007/BF01232041

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