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Two letters on quaternions and modular forms (modp)

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Abstract

We present two letters of J-P. Serre to Tate and to Kazhdan. The first indicates an approach to modular forms (modp) through quaternions. The second discusses the theory of representations of local and adelic groups associated to these quaternions in characteristicp.

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References

  1. L. Barthel and R. Livné,Modular representations of GL2 of a local field: the ordinary, unramified case, Journal of Number Theory55 (1995), 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Barthel and R. Livné,Irreducible modular representations of GL2 of a local field, Duke Mathematical Journal75 (1994), 261–292.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Deligne,Les constantes des équations fonctionnelles des fonctions L, in Lecture Notes in Mathematics349, Springer-Verlag, Berlin, 1973, pp. 501–597.

    Google Scholar 

  4. F. Diamond,The refined conjecture of Serre, inElliptic Curves, Modular Forms, & Fermat's Last Theorem (J. Coates and S.T. Yau, eds.), International Press, Cambridge, 1995, pp. 22–37.

    Google Scholar 

  5. F. Diamond and R. Taylor,Non-optimal levels of modl modular representations, Inventiones mathematicae115 (1994), 435–462.

    Article  MATH  MathSciNet  Google Scholar 

  6. B.W. Jordan and R. Livné,Integral Hodge theory and congruences between modular forms, Duke Mathematical Journal80 (1995), 419–484.

    Article  MATH  MathSciNet  Google Scholar 

  7. N. Katz,p-adic properties of modular schemes and modular forms, in Lecture Notes in Mathematics350, Springer-Verlag, Berlin, 1973, pp 69–190.

    Google Scholar 

  8. K.A. Ribet,Bimodules and abelian surfaces, Advanced Studies in Pure Mathematics17, Academic Press, New York, 1989, pp. 359–407.

    Google Scholar 

  9. K.A. Ribet,Report on mod l representations of\(Gal(\bar Q/Q)\), Proceedings of Symposia in Pure Mathematics55 (1994), Part II, 639–676.

    MathSciNet  Google Scholar 

  10. G. Robert,Congruences entre séries d'Eisenstein dans le cas supersingulier, Inventiones mathematicae61 (1980), 103–158.

    Article  MATH  MathSciNet  Google Scholar 

  11. J-P. Serre, Sur les représentations modulaires de degré 2 de\(Gal(\bar Q/Q)\), Duke Mathematical Journal54 (1987), 179–230.

    Article  MATH  MathSciNet  Google Scholar 

  12. J-P. Serre,Résumé des cours de 1987–1988, Annuaire du Collège de France (1988), 79–82.

  13. J. Teitelbaum,Modular representations of PGL2 and automorphic forms for Shimura curves, Inventiones mathematicae113 (1993), 561–580.

    Article  MATH  MathSciNet  Google Scholar 

  14. M.-F. Vignéras,Représentations modulaires de GL(2,F)en caractéristique l, F corps p-adique, p ≠l, Compositio Mathematica72 (1989), 33–66.

    MATH  MathSciNet  Google Scholar 

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Serre, JP., Livné, R. Two letters on quaternions and modular forms (modp). Israel J. Math. 95, 281–299 (1996). https://doi.org/10.1007/BF02761043

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  • DOI: https://doi.org/10.1007/BF02761043

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