Residually reductible representations and modular forms

Skinner, C.M.; Wiles, Andrew J.

Publications Mathématiques de l'IHÉS, Tome 89 (1999), pp. 5-126.

[C] H. Carayol, Sur les représentations ℓ-adiques associées aux formes modulaires de Hilbert, Ann. Sci. Ec. Norm. Sup. IV, Ser. 19 (1986), 409-468. | Numdam | MR | Zbl

[Ca] P. Cartier, La conjecture locale de Langlands pour GL(2) et la démonstration de Ph. Kutzko, in Bourbaki Seminar, Vol. 1979/1980, Lecture Notes in Math., 842, Springer, (1981), 112-138. | Numdam | MR | Zbl

[Ch] C.-L. Chai, Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces, Ann. of Math. (2) 131 (1990), no. 3, 541-554. | MR | Zbl

[Co] J. Coates, p-adic L-functions and Iwasawa's theory, in Algebraic number fields : L-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), Academic Press (1977), 269-353. | MR | Zbl

[De] P. Deligne, Formes modulaires et représentations de GL(2), in Modular functions of one variable, II, Lecture Notes in Math., 349, Springer, (1973), 55-105. | MR | Zbl

[D-R] P. Deligne, K. Ribet, Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), no. 3, 227-286. | MR | Zbl

[DRS] B. De Smit, K. Rubin, R. Schoof, Criteria for complete intersections, in Modular forms and Fermat's Last Theorem, Springer (1997), 343-356. | MR | Zbl

[D1] F. Diamond, On deformation rings and Hecke rings, Ann. of Math. (2), 144 (1996), no. 1, 137-166. | MR | Zbl

[D2] F. Diamond, The Taylor-Wiles construction and multiplicity one, Invent. Math. 128, (1997), no. 2, 379-391. | MR | Zbl

[DT] F. Diamond, R. Taylor, Non optimal levels of mod ℓ modular representations, Invent. Math. 115 (1994), no. 3, 435-462. | MR | Zbl

[FM] J.-M. Fontaine, B. Mazur, Geometric Galois representations, in Elliptic Curves, modular forms, and Fermat's Last Theorem (Hong Kong, 1993), Internat. Press (1995), 41-78. | MR | Zbl

[Ge] S. Gelbart, Automorphic Forms on Adele Groups, Annals of Math. Studies, Vol. 83, Princeton University Press (1975). | MR | Zbl

[GL] P. Gérardin, J.-P. Labesse, The solution of a base change problem for GL(2) (following Langlands, Saito, Shintani), in Automorphic forms, representations and L-functions, Proc. Symp. Pure Math., XXXIII, part 2, 115-133. | Zbl

[G] A. Grothendieck, Éléments de la géométrie algébrique IV, Étude locale des schémas et des morphismes de schémas (deuxième partie), Publ. Math. de l'IHES 24 (1965). | Numdam | Zbl

[H1] H. Hida, On p-adic Hecke algebras for GL2 over totally real fields, Ann. of Math. (2) 128, (1988), no. 2, 295-384. | MR | Zbl

[H2] H. Hida, On nearly ordinary Hecke algebras for GL(2) over totally real fields, in Algebraic number theory, Adv. Stud. Pure Math., 17, Academic Press (1989) 139-169. | MR | Zbl

[H3] H. Hida, Nearly ordinary Hecke algebras and Galois representations of several variables, in Algebraic analysis, geometry, and number theory (Baltimore, MD 1988), John Hopkins Univ. Press (1989), 115-134. | MR | Zbl

[I] K. Iwasawa, On Zℓ extensions of algebraic number fields, Ann. of Math. (2) 98 (1973), 246-326. | MR | Zbl

[J-L] H. Jacquet, R. Langlands, Automorphic forms on GL(2), Lecture Notes in Math., 114, Springer (1970). | MR | Zbl

[Ku] P. Kutzko, The Langlands conjecture for GL2 of a local field, Ann. of Math. (2) 112, (1980), no. 2, 381-412. | Zbl

[Mat] H. Matsumura, Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge Univ. Press (1989). | MR | Zbl

[M] B. Mazur, Deforming Galois representations, in Galois Groups over Q, vol. 16, MSRI Publications, Springer (1989). | MR | Zbl

[N] M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, n° 13, Interscience Publishers (1962). | MR | Zbl

[R] R. Ramakrishna, On a variation of Mazur's deformation functor, Comp. Math. 87 (1993), 269-286. | Numdam | MR | Zbl

[Ray] M. Raynaud, Théorèmes de Lefschetz en cohomologie cohérent et en cohomologie étale, Bull. Soc. Math. France, Mém. no. 41. Supplément au Bull. Soc. Math. France, Tome 103, Société Mathématique de France (1975). | Numdam | MR | Zbl

[Ri] K. Ribet, Congruence relations between modular forms, Proc. Int. Cong. of Math. 17 (1983), 503-514. | MR | Zbl

[Sch] M. Schlessinger, Functors on Artin rings, Trans. AMS 130 (1968), 208-222. | MR | Zbl

[Se] J.-P. Serre, Sur le résidu de la function zêta p-adique d'un corps de nombres, C.R. Acad. Sc. Paris 287, Serie A (1978), 183-188. | MR | Zbl

[Shi] H. Shimizu, Theta series and modular forms on GL2, J. Math. Soc. Japan 24 (1973), 638-683. | MR | Zbl

[Sh] G. Shimura, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637-679. | MR | Zbl

[SW] C. Skinner, A. Wiles, Ordinary representations and modular forms, Proc. Nat. Acad. Sci. USA 94 (1997), no. 20, 10520-10527. | MR | Zbl

[TW] R. Taylor, A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2), 141 (1995), no. 3, 553-572. | MR | Zbl

[Wal] M. Waldschmidt, A lower bound for the p-adic rank of the units of an algebraic number field, in Topics in classical number theory, Vol. I, II (Budapest, 1981), Colloq. Math. Soc. János Bolyai, 34, North-Holland (1984), 1617-1650. | MR | Zbl

[Wa] L. Washington, The non-p-part of the class number in a cyclotomic Zp-extension, Invent. Math. 49 (1978), no. 1, 87-97. | MR | Zbl

[We] A. Weil, Basic Number Theory, Springer (1967). | MR | Zbl

[W1] A. Wiles, Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. (2), 142 (1995), 443-551. | MR | Zbl

[W2] A. Wiles, On ordinary λ-adic representations associated to modular forms, Invent. Math. 94 (1988), 529-573. | MR | Zbl

[W3] A. Wiles, On p-adic representations for totally real fields, Ann. of Math. (2), 123 (1986), 407-456. | MR | Zbl