Duke Mathematical Journal

Congruences between cusp forms: the $(p,p)$ case

Chandrashekhar Khare
Source: Duke Math. J. Volume 80, Number 3 (1995), 631-667.
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Primary Subjects: 11F33
Secondary Subjects: 11F32, 11F85
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077246289
Mathematical Reviews number (MathSciNet): MR1412447
Zentralblatt MATH identifier: 0857.11021
Digital Object Identifier: doi:10.1215/S0012-7094-95-08022-3

References

[AL] A. Atkin and J. Lehner, Hecke operators on $\Gamma \sb0(m)$, Math. Ann. 185 (1970), 134–160.
Mathematical Reviews (MathSciNet): MR42:3022
Zentralblatt MATH: 0177.34901
Digital Object Identifier: doi:10.1007/BF01359701
[ALi] A. Atkin and W. Li, Twists of newforms and pseudo-eigenvalues of $W$-operators, Invent. Math. 48 (1978), no. 3, 221–243.
Mathematical Reviews (MathSciNet): MR80a:10040
Zentralblatt MATH: 0369.10016
Digital Object Identifier: doi:10.1007/BF01390245
[AS] A. Ash and G. Stevens, Modular forms in characteristic $l$ and special values of their $L$-functions, Duke Math. J. 53 (1986), no. 3, 849–868.
Mathematical Reviews (MathSciNet): MR88h:11036
Zentralblatt MATH: 0618.10026
Digital Object Identifier: doi:10.1215/S0012-7094-86-05346-9
Project Euclid: euclid.dmj/1077305204
[BLR] N. Boston, H. W. Lenstra, and K. Ribet, Quotients of group rings arising from two-dimensional representations, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 4, 323–328.
Mathematical Reviews (MathSciNet): MR92c:11057
Zentralblatt MATH: 0718.16018
[C] H. Carayol, Sur les représentations galoisiennes modulo $l$ attachées aux formes modulaires, Duke Math. J. 59 (1989), no. 3, 785–801.
Mathematical Reviews (MathSciNet): MR91b:11058
Zentralblatt MATH: 0703.11027
Digital Object Identifier: doi:10.1215/S0012-7094-89-05937-1
Project Euclid: euclid.dmj/1077308170
[C1] H. Carayol, Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 3, 409–468.
Mathematical Reviews (MathSciNet): MR89c:11083
Zentralblatt MATH: 0616.10025
[Cr] J. Cremona, Algorithms for modular elliptic curves, Cambridge University Press, Cambridge, 1992.
Mathematical Reviews (MathSciNet): MR93m:11053
Zentralblatt MATH: 0758.14042
[DT] F. Diamond and R. Taylor, Nonoptimal levels of mod $l$ modular representations, Invent. Math. 115 (1994), no. 3, 435–462.
Mathematical Reviews (MathSciNet): MR95c:11060
Zentralblatt MATH: 0847.11025
Digital Object Identifier: doi:10.1007/BF01231768
[E] B. Edixhoven, The weight in Serre's conjectures on modular forms, Invent. Math. 109 (1992), no. 3, 563–594.
Mathematical Reviews (MathSciNet): MR93h:11124
Zentralblatt MATH: 0777.11013
Digital Object Identifier: doi:10.1007/BF01232041
[G] F. Gouvêa, Arithmetic of $p$-adic modular forms, Lecture Notes in Mathematics, vol. 1304, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR91e:11056
Zentralblatt MATH: 0641.10024
[Ge] S. Gelbart, Automorphic forms on adèle groups, Annals of Mathematics Studies, vol. 83, Princeton University Press, Princeton, N.J., 1975.
Mathematical Reviews (MathSciNet): MR52:280
Zentralblatt MATH: 0329.10018
[Gr] B. Gross, A tameness criterion for Galois representations associated to modular forms (mod $p$), Duke Math. J. 61 (1990), no. 2, 445–517.
Mathematical Reviews (MathSciNet): MR91i:11060
Zentralblatt MATH: 0743.11030
Digital Object Identifier: doi:10.1215/S0012-7094-90-06119-8
Project Euclid: euclid.dmj/1077296826
[H] H. Hida, Galois representations into $\rm GL\sb 2(\bf Z\sb p[[X]])$ attached to ordinary cusp forms, Invent. Math. 85 (1986), no. 3, 545–613.
Mathematical Reviews (MathSciNet): MR87k:11049
Zentralblatt MATH: 0612.10021
Digital Object Identifier: doi:10.1007/BF01390329
[H1] H. Hida, Modular $p$-adic $L$ functions and $p$-adic Hecke algebras, to appear in Sugaku Expositions.
Mathematical Reviews (MathSciNet): MR1197555
[H2] H. Hida, Geometric modular forms, 1992, CIMPA Summer School.
[J] N. Jochnowitz, A study of the local components of the Hecke algebra mod $l$, Trans. Amer. Math. Soc. 270 (1982), no. 1, 253–267.
Mathematical Reviews (MathSciNet): MR83e:10033a
Zentralblatt MATH: 0536.10021
Digital Object Identifier: doi:10.2307/1999771
[K] C. Khare, Congruences between cusp forms, Ph.D. thesis, California Institute of Technology, 1995.
[Ka] N. Katz, Higher congruences between modular forms, Ann. of Math. (2) 101 (1975), 332–367.
Mathematical Reviews (MathSciNet): MR54:5120
Zentralblatt MATH: 0356.10020
Digital Object Identifier: doi:10.2307/1970994
[La] S. Lang, Introduction to modular forms, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR55:2751
Zentralblatt MATH: 0344.10011
[Li] S. Ling, Congruences between cusp forms and the geometry of Jacobians of modular curves, Math. Ann. 295 (1993), no. 1, 111–133.
Mathematical Reviews (MathSciNet): MR94a:11063
Zentralblatt MATH: 0789.14027
Digital Object Identifier: doi:10.1007/BF01444879
[LO] S. Ling and J. Oesterlé, The Shimura subgroup of $J\sb 0(N)$, Astérisque (1991), no. 196-197, 6, 171–203 (1992).
Mathematical Reviews (MathSciNet): MR93b:14038
Zentralblatt MATH: 0781.14015
[M] B. Mazur, Deforming Galois representations, Galois groups over $\bf Q$ (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer, New York, 1989, pp. 385–437.
Mathematical Reviews (MathSciNet): MR90k:11057
Zentralblatt MATH: 0714.11076
[M1] B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 33–186 (1978).
Mathematical Reviews (MathSciNet): MR80c:14015
Zentralblatt MATH: 0394.14008
Digital Object Identifier: doi:10.1007/BF02684339
[MR] B. Mazur and K. Ribet, Two-dimensional representations in the arithmetic of modular curves, Astérisque (1991), no. 196-197, 6, 215–255 (1992).
Mathematical Reviews (MathSciNet): MR93d:11056
Zentralblatt MATH: 0780.14015
[MW] B. Mazur and A. Wiles, Class fields of abelian extensions of $\bf Q$, Invent. Math. 76 (1984), no. 2, 179–330.
Mathematical Reviews (MathSciNet): MR85m:11069
Zentralblatt MATH: 0545.12005
Digital Object Identifier: doi:10.1007/BF01388599
[Mi] J. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press Inc., Boston, MA, 1986.
Mathematical Reviews (MathSciNet): MR88e:14028
Zentralblatt MATH: 0613.14019
[R] K. Ribet, Congruence relations between modular forms, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), PWN, Warsaw, 1984, pp. 503–514.
Mathematical Reviews (MathSciNet): MR87c:11045
Zentralblatt MATH: 0575.10024
[R1] K. Ribet, On modular representations of $\rm Gal(\overline\bf Q/\bf Q)$ arising from modular forms, Invent. Math. 100 (1990), no. 2, 431–476.
Mathematical Reviews (MathSciNet): MR91g:11066
Zentralblatt MATH: 0773.11039
Digital Object Identifier: doi:10.1007/BF01231195
[R2] K. Ribet, Report on mod $l$ representations of $\rm Gal(\overline\bf Q/\bf Q)$, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 639–676.
Mathematical Reviews (MathSciNet): MR95d:11056
Zentralblatt MATH: 0822.11034
[R3] K. Ribet, Raising the levels of modular representations, Séminaire de Théorie des Nombres, Paris 1987–88, Progr. Math., vol. 81, Birkhäuser Boston, Boston, MA, 1990, pp. 259–271.
Mathematical Reviews (MathSciNet): MR91g:11055
Zentralblatt MATH: 0705.11030
[Ra] M. Raynaud, Schémas en groupes de type $(p,\dots, p)$, Bull. Soc. Math. France 102 (1974), 241–280.
Mathematical Reviews (MathSciNet): MR54:7488
Zentralblatt MATH: 0325.14020
[S] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971.
Mathematical Reviews (MathSciNet): MR47:3318
Zentralblatt MATH: 0221.10029
[Se] J.-P. Serre, Sur les représentations modulaires de degré $2$ de $\rm Gal(\overline\bf Q/\bf Q)$, Duke Math. J. 54 (1987), no. 1, 179–230.
Mathematical Reviews (MathSciNet): MR88g:11022
Zentralblatt MATH: 0641.10026
Digital Object Identifier: doi:10.1215/S0012-7094-87-05413-5
Project Euclid: euclid.dmj/1077305511
[Se1] J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), no. 4, 259–331.
Mathematical Reviews (MathSciNet): MR52:8126
Zentralblatt MATH: 0235.14012
Digital Object Identifier: doi:10.1007/BF01405086
[Se2] J.-P. Serre, Trees, Springer-Verlag, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82c:20083
Zentralblatt MATH: 0548.20018
[Se3] J.-P. Serre, Le problème des groupes de congruence pour SL2, Ann. of Math. (2) 92 (1970), 489–527.
Mathematical Reviews (MathSciNet): MR42:7671
Zentralblatt MATH: 0239.20063
Digital Object Identifier: doi:10.2307/1970630
[W] A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551.
Mathematical Reviews (MathSciNet): MR96d:11071
Zentralblatt MATH: 0823.11029
Digital Object Identifier: doi:10.2307/2118559

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