Integral Hodge theory and congruences between modular forms
Bruce W. Jordan and Ron Livné
Source: Duke Math. J. Volume 80, Number 2
(1995), 419-484.
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References
[1] L. Barthel and R. Livné, Modular representations of $GL_2$ of a local field: the ordinary, unramified case, to appear in J. Number Theory.
Mathematical Reviews (MathSciNet): MR1361556
Zentralblatt MATH: 0841.11026
Digital Object Identifier: doi:10.1006/jnth.1995.1124
[2] I. N. Bernstein and A. V. Zelevinskii, Representations of the group $GL(n,F),$ where $F$ is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70, Translation in Russian Math Surveys 31(3)(1976), 1–68.
Mathematical Reviews (MathSciNet): MR54:12988
[3] H. Brandt, Zur Zahlentheorie der Quaternionen, Jber. Deutsch. Math. Verein. 53 (1943), 23–57.
Mathematical Reviews (MathSciNet): MR8,198b
Zentralblatt MATH: 0028.10802
[4] G. E. Bredon, Equivariant cohomology theories, Lecture Notes in Mathematics, No. 34, Springer-Verlag, Berlin, 1967.
Mathematical Reviews (MathSciNet): MR35:4914
Zentralblatt MATH: 0162.27202
[5] 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
[6] I. V. Cerednik, Uniformization of algebraic curves by discrete arithmetic subgroups of ${\rm PGL}\sb{2}(k\sb{w})$ with compact quotient spaces, Mat. Sb. (N.S.) 100(142) (1976), no. 1, 59–88, 165, Translation in Math. USSR Sb. 29(1976), 55–78.
Mathematical Reviews (MathSciNet): MR58:10909
[7] P. Deligne and J.-P. Serre, Formes modulaires de poids $1$, Ann. Sci. École Norm. Sup. (4) 7 (1974), 507–530 (1975).
Mathematical Reviews (MathSciNet): MR52:284
Zentralblatt MATH: 0321.10026
[8] F. Diamond, Congruence primes for cusp forms of weight $k\ge 2$, Astérisque (1991), no. 196-197, 6, 205–213 (1992).
Mathematical Reviews (MathSciNet): MR93b:11051
Zentralblatt MATH: 0783.11022
[9] 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
[10] V. G. Drinfeld, Coverings of $p$-adic symmetric domains, Funkcional. Anal. i Priložen. 10 (1976), no. 2, 29–40, Translation in Functional Anal. Appl. 10(1976), 107–115.
Mathematical Reviews (MathSciNet): MR54:10281
Zentralblatt MATH: 0346.14010
[11] B. Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex, Comment. Math. Helv. 17 (1945), 240–255.
Mathematical Reviews (MathSciNet): MR7,138f
Zentralblatt MATH: 0061.41106
Digital Object Identifier: doi:10.1007/BF02566245
[12]1 M. Eichler, The basis problem for modular forms and the traces of the Hecke operators, Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1973, 75–151. Lecture Notes in Math., Vol. 320.
Mathematical Reviews (MathSciNet): MR58:5521a
Zentralblatt MATH: 0258.10013
Digital Object Identifier: doi:10.1007/978-3-540-38509-7_4
[12]2 M. Eichler, Correction to: “The basis problem for modular forms and the traces of the Hecke operators” (Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, 1972), pp. 75–151, Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973), Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1975, 145–147. Lecture Notes in Math., Vol. 476.
Mathematical Reviews (MathSciNet): MR58:5521b
[13]1 M. Eichler, Zur Zahlentheorie der Quaternionen-Algebren, J. Reine Angew. Math. 195 (1955), 127–151 (1956).
Mathematical Reviews (MathSciNet): MR18,297c
Zentralblatt MATH: 0068.03303
Digital Object Identifier: doi:10.1515/crll.1955.195.127
[13]2 M. Eichler, Berichtigung zu der Arbeit “Zur Zahlentheorie der Quaternionen-Algebren”, J. Reine Angew. Math. 197 (1957), 220.
Mathematical Reviews (MathSciNet): MR19,17e
Zentralblatt MATH: 0068.03303
[14] H. Garland, $p$-adic curvature and the cohomology of discrete subgroups of $p$-adic groups, Ann. of Math. (2) 97 (1973), 375–423.
Mathematical Reviews (MathSciNet): MR47:8719
Zentralblatt MATH: 0262.22010
Digital Object Identifier: doi:10.2307/1970829
JSTOR: links.jstor.org
[15] S. Gelbart, Automorphic forms on adèle groups, Princeton University Press, Princeton, N.J., 1975.
Mathematical Reviews (MathSciNet): MR52:280
Zentralblatt MATH: 0329.10018
[16] S. Gelbart and H. Jacquet, Forms of ${\rm GL}(2)$ from the analytic point of view, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 213–251.
Mathematical Reviews (MathSciNet): MR81e:10024
Zentralblatt MATH: 0409.22013
[17] A. Grothendieck, Groupes de monodromie en géométrie algébrique. I, Lecture Notes in Mathematics, vol. 288, Springer-Verlag, Berlin, 1972.
Mathematical Reviews (MathSciNet): MR50:7134
Zentralblatt MATH: 0237.00013
[18] H. Hida, On $p$-adic Hecke algebras for ${\rm GL}\sb 2$ over totally real fields, Ann. of Math. (2) 128 (1988), no. 2, 295–384.
Mathematical Reviews (MathSciNet): MR89m:11046
Zentralblatt MATH: 0658.10034
Digital Object Identifier: doi:10.2307/1971444
JSTOR: links.jstor.org
[19] H. Hijikata, A. K. Pizer, and T. R. Shemanske, The basis problem for modular forms on $\Gamma\sb 0(N)$, Mem. Amer. Math. Soc. 82 (1989), no. 418, vi+159.
Mathematical Reviews (MathSciNet): MR90d:11056
Zentralblatt MATH: 0689.10034
[20] H. Jacquet and R. P. Langlands, Automorphic Forms on ${\rm GL}(2)$, Lecture Notes in Mathematics, vol. 114, Springer-Verlag, Berlin, 1970.
Mathematical Reviews (MathSciNet): MR53:5481
Zentralblatt MATH: 0236.12010
[21] B. W. Jordan and R. Livné, Conjecture “epsilon” for weight $k>2$, Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 51–56.
Mathematical Reviews (MathSciNet): MR90d:11057
Zentralblatt MATH: 0675.10020
Digital Object Identifier: doi:10.1090/S0273-0979-1989-15758-3
Project Euclid: euclid.bams/1183555123
[22] B. W. Jordan and R. Livné, Local Diophantine properties of Shimura curves, Math. Ann. 270 (1985), no. 2, 235–248.
Mathematical Reviews (MathSciNet): MR86g:11036
Zentralblatt MATH: 0536.14018
Digital Object Identifier: doi:10.1007/BF01456184
[23] B. W. Jordan and R. Livné, On the Néron model of Jacobians of Shimura curves, Compositio Math. 60 (1986), no. 2, 227–236.
Mathematical Reviews (MathSciNet): MR88c:11039
Zentralblatt MATH: 0609.14018
[24] S. Lang, Introduction to modular forms, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR55:2751
Zentralblatt MATH: 0344.10011
[25] 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
[26] M. Raynaud, Spécialisation du foncteur de Picard, Inst. Hautes Études Sci. Publ. Math. (1970), no. 38, 27–76.
Mathematical Reviews (MathSciNet): MR44:227
Zentralblatt MATH: 0207.51602
Digital Object Identifier: doi:10.1007/BF02684651
[27] K. A. Ribet, Bimodules and abelian surfaces, Algebraic number theory, Adv. Stud. Pure Math., vol. 17, Academic Press, Boston, MA, 1989, pp. 359–407.
Mathematical Reviews (MathSciNet): MR92a:11070
Zentralblatt MATH: 0742.11033
[28] K. A. Ribet, On the component groups and the Shimura subgroup of $J\sb 0(N)$, Séminaire de Théorie des Nombres, 1987–1988 (Talence, 1987–1988), Univ. Bordeaux I, Talence, 19??, Exp. No. 6, 10.
Mathematical Reviews (MathSciNet): MR91b:11070
Zentralblatt MATH: 0691.14009
[29] K. A. 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
[30] K. A. 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
[31] J.-P. Serre, Arbres, Amalgames, $SL_{2}$, Société Mathematique de France, Paris, 1982.
[32] J.-P. Serre, Corps locaux, Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR50:7096
[33] J.-P. Serre, May 27 1979, Lettre to J.-M. Fontaine.
[34] 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
[35] H. Shimizu, On zeta functions of quaternion algebras, Ann. of Math. (2) 81 (1965), 166–193.
Mathematical Reviews (MathSciNet): MR30:1998
Zentralblatt MATH: 0201.37903
Digital Object Identifier: doi:10.2307/1970389
JSTOR: links.jstor.org
[36] 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
[37] R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), no. 2, 265–280.
Mathematical Reviews (MathSciNet): MR90m:11176
Zentralblatt MATH: 0705.11031
Digital Object Identifier: doi:10.1007/BF01388853
[38] J. Teitelbaum, Modular representations of ${\rm PGL}\sb 2$ and automorphic forms for Shimura curves, Invent. Math. 113 (1993), no. 3, 561–580.
Mathematical Reviews (MathSciNet): MR94h:11049
Zentralblatt MATH: 0806.11027
Digital Object Identifier: doi:10.1007/BF01244318
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