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On modular representations of\((\bar Q/Q)\) arising from modular forms

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References

  1. Atkin, A.O.L., Lehner, J.: Hecke operators onF o(m). Math. Ann.185, 134–160 (1970)

    Google Scholar 

  2. Carayol, H.: Sur la mauvaise réduction des courbes de Shimura. Compos. Math.59, 151–230 (1986)

    Google Scholar 

  3. Cerednik, I.V.: Uniformization of algebraic curves by discrete arithmetic subgroups of PGL2(k w ) with compact quotients (in Russian). Math. Sb.100, 59–88 (1976). Translation in Math. USSR Sb.29, 55–78 (1976)

    Google Scholar 

  4. Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. (Lecture Notes in Math. Vol.349, pp. 143–316.) Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

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

    Google Scholar 

  6. Deuring, M.: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Semin. Univ. Hamb.14, 197–272 (1941)

    Google Scholar 

  7. Drinfeld, V.G.: Coverings ofp-adic symmetric retions (in Russian). Funkts. Anal. Prilozn10, 29–40 (1976). Translation in Funct. Anal. Appl.10, 107–115 (1976)

    Google Scholar 

  8. Edixhoven, S.J.: L'action de l'algèbre de Hecke sur les groupes de composantes des jacobiennes des courbes modulaires est “Eisenstein”. Preprint

  9. Eichler, M.: Quadratische Formen und Modulfunktionen. Acta Arith.4, 217–239 (1958)

    Google Scholar 

  10. Frey, G.: Links between stable elliptic curves and certain diophantine equations. Ann. Univ. Sarav., Ser Math.1, 1–40 (1986)

    Google Scholar 

  11. Grothendieck, A.: SGA7 I, exposé IX. (Lecture Notes in Math. Vol.288, pp. 313–523.) Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  12. Jacquet, H., Langlands, R.P.: Automorphic forms on GL(2). (Lecture Notes in Math. Vol.114). Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  13. Jordan, B., Livné, R.: local diophantine properties of Shimura curves. Math. Ann.270, 235–248 (1985)

    Google Scholar 

  14. Jordan, B., Livné, R.: On the Néron model of Jacobians of Shimura curves. Compos. Math.60, 227–236 (1986)

    Google Scholar 

  15. Katz, N.M., Mazur, B.: Arithmetic Moduli of Elliptic Curves. Ann. Math. Stud.108 (1985)

  16. Kurihara, A.: On some examples of equations defining Shimura curves and the Mumford uniformization. J. Fac., Sci., Univ. Tokyo, Sec. IA25, 277–300 (1979)

    Google Scholar 

  17. Langlands, R.P.: Some contemporary problems with origins in the Jugendtraum. Proc. Symp. Pure Math.28, 401–418 (1976)

    Google Scholar 

  18. Mazur, B.: Modular curves and the Eisenstein ideal. Publ. Math., Inst. Hautes Etud. Sci.47, 33–186 (1977)

    Google Scholar 

  19. Mazur, B.: Rational isogenies of prime degree. Invent. Math.44, 129–162 (1978)

    Google Scholar 

  20. Mazur, B.: Letter to J-F. Mestre (16 August 1985)

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

  22. Milne, J.: Etude d'une classe d'isogénie. In: Variétés de Shimura et FonctionsL, Breen, L., Labesse, J-P. (eds.) Publ. Math. Univ. Paris VII6, 73–81 (1979)

  23. Oda, T.: The first de Rham cohomology group and Dieudonné modules. Ann. Sci. Ec. Norm. Sup. IV, Ser.2, 63–135 (1969)

    Google Scholar 

  24. Raynaud, M.: Specialisation du foncteur de Picard. Publ. Math., Inst. Hautes Etud. Sci.38, 27–76 (1970)

    Google Scholar 

  25. Raynaud, M.: Schémas en groupes de type (p,...p). Bull. Soc. Math. France102, 241–280 (1974)

    Google Scholar 

  26. Ribet, K.: Sur les variétés abéliennes à multiplications réelles. C.R. Acad. Sc. Paris, Sér. A291, 121–123 (1980)

    Google Scholar 

  27. Ribet, K.: Modp Hecke operators and congruences between modular forms. Invent. Math.71, 193–205 (1983)

    Google Scholar 

  28. Ribet, K.: Congruence relations between modular forms. Proc. Int. Congr. Math. pp. 503–514 (1983)

  29. Ribet, K.: Bimodules and abelian surfaces. Adv. Stud. Pure Math.17, 359–407 (1989)

    Google Scholar 

  30. Ribet, K.: On the component groups and the Shimura subgroup ofJ o (N). Sém. Th. Nombres, Université Bordeaux, 1987–88

  31. Ribet, K.: Raising the levels of modular representations, Séminaire de Théorie des Nombres, Paris 1987–88. Progr. Math.81, 259–271 (1990)

    Google Scholar 

  32. Serre, J.-P., Complex multiplication. In: Algebraic Number Theory, Cassels, JWS, Fröhlich, A. (eds.). Washington, DC: Thompson Book Company 1967

    Google Scholar 

  33. Serre, J-P.: Arbres, Amalgames, SL2. Astérisque46 (1977). English translation: Trees. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  34. Serre, J-P.: Lettre à J-F. Mestre (13 août 1985). Contemp. Math.67, 263–268 (1987)

    Google Scholar 

  35. Serre, J-P.: Sur les représentations modulaires de degré 2 de Gal\((\bar Q/Q)\). Duke Math. J.54, 179–230 (1987)

    Google Scholar 

  36. Shimizu, H.: On the zeta functions of quaternion algebras. Ann. Math.81, 166–193 (1965)

    Google Scholar 

  37. Shimura, G.: Construction of class fields and zeta functions of algebraic curves. Ann. Math.85, 58–159 (1967)

    Google Scholar 

  38. Shimura, G.: On canonical models of arithmetic quotients of bounded symmetric domains. Ann. Math.91, 144–222 (1970)

    Google Scholar 

  39. Shimura, G.: Introduction to the Airthmetic Theory of Automorphic Functions. Princeton: Princeton University Press 1971

    Google Scholar 

  40. Tate, J.: Endomorphisms of abelian varieties over finite fields. Invent. Math.2, 134–144 (1966)

    Google Scholar 

  41. Vignéras, M-F.: Arithmétíque des Algèbres de Quaternions. (Lecture Notes in Math., Vol.800. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  42. Waterhouse, W.C.: Abelian varieties over finite fields. Ann. Sci. Ec. Norm. Sup. IV. Ser.2, 521–560 (1969)

    Google Scholar 

  43. [EGAIV] Grothendieck, A.: Etude locale des schémas et des morphismes de schémas (quatrième partie). Publ. Math, Inst. Hautes Etud. Sci.32, 5–361 (1967)

    Google Scholar 

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  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    K. A. Ribet

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Ribet, K.A. On modular representations of\((\bar Q/Q)\) arising from modular forms. Invent Math 100, 431–476 (1990). https://doi.org/10.1007/BF01231195

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