Rational elliptic curves are modular

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1. [1] P. Berthelot - Altérations de variétés algébriques. Séminaire Bourbaki, 1995-96, exposé 815, Astérisque241, S.M.F. (1997), 273-311. Zbl0924.14007MR1472543
2. [2] C. Breuil - Schémas en groupes et modules filtrés. C. R. Acad. Sci. Paris328 (1999), 93-97. Zbl0924.14025MR1669039
3. [3] C. Breuil - Groupes p-divisibles, groupes finis et modules filtrés. Ann. of Math. (2) 152 (2000), no. 2, 489-549. Mathematics. Zbl1042.14018MR1804530
4. [4] C. Breuil, B. Conrad, F. Diamond, R. Taylor - On the modularity of elliptic curves over Q: wild 3-adic exercises. J. Amer. Math. Soc.14 (2001), no. 4, 843-939. Zbl0982.11033MR1839918
5. [5] C. Breuil, A. Mezard - Multiplicités modulaires et représentations de GL2(Zp) et de Gal(Qp/Qp) en l = p. Preprint, June 2000, Orsay. 
6. [6] C.J. Bushnell - Smooth representations of p-adic groups: the role of compact open subgroups. Proceedings of the international congress of mathematicians, Vol. 1, 2 (Zürich, 1994), 770-779, Birkhaüser, Basel, 1995. Zbl0856.22021MR1403977
7. [7] K. Buzzard, M. Dickinson, N. Shepherd-Barron, R. Taylor - On icosahedral Artin representations. Duke Math. J.109 (2001), no. 2, 283-318. Zbl1015.11021MR1845181
8. [8] K. Buzzard, R. Taylor - Companion forms and weight one forms. Ann. of Math. (2) 149 (1999), no. 3, 905-91 Zbl0965.11019MR1709306
9. [9] H. Carayol - Sur les représentations l-adiques associées aux formes modulaires de Hilbert. Ann. Sci. Éc. Norm. Sup.19 (1986), 409-468. Zbl0616.10025MR870690
10. [10] L. Clozel - Motifs et formes automorphes. Automorphic forms, Shimura varieties, and L-functions, Vol. I, edited by L. Clozel and J.S. Milne, Perspectives in Mathematics10, Academic Press (1990), 77-159. Zbl0705.11029MR1044819
11. [11] P. Colmez, J.-M. Fontaine - Construction des représentations p-adiques semi-stables. Invent. Math.140 (2000), no. 1, 1-43. Zbl1010.14004MR1779803
12. [12] B. Conrad - Finite group schemes over bases with low ramification. Compositio Math.119 (1999), 239-320. Zbl0984.14015MR1727133
13. [13] B. Conrad - Ramified deformation problems. Duke Math. J.97 (1999), 439-513. Zbl0997.11042MR1682986
14. [14] B. Conrad, F. Diamond, R. Taylor - Modularity of certain potentially Barsotti-Tate Galois representations. J.A.M.S.12 (1999), 521-567. Zbl0923.11085MR1639612
15. [15] G. Cornell, J. Silverman, G. Stevens, EDITORS - Modular Forms and Fermat's Last TheoremSpringer-Verlag, 1997. Zbl0878.11004MR1638473
16. [16] H. Darmon - A proof of the full Shimura-Taniyama-Weil conjecture is announced. Notices of the A.M.S., December 1999. Zbl1009.11036MR1723249
17. [17] H. Darmon, F. Diamond, R. Taylor - Fermat's Last Theorem. Elliptic curves, modular forms and Fermat's last theorem (Hong Kong, 1993). Second edition. International Press, Cambridge, MA, 1997, 2-140. Zbl0877.11035MR1605752
18. [18] P. Deligne - Formes modulaires et représentations l-adiques. Séminaire Bourbaki, 1968-69, exposé 355, Lecture Notes in Mathematics179, Springer (1969), 139-172. Zbl0206.49901
19. [19] P. Deligne - Formes modulaires et représentations de GL(2). Antwerp II, Lecture Notes in Math.349, Springer (1973), 55-106. Zbl0271.10032MR347738
20. [20] B. De Smit, H. Lenstra - Explicit construction of universal deformation rings. In [15], 313-326. Zbl0907.13010MR1638482
21. [21] B. De Smit, K. Rubin, R. Schoof - Criteria for complete intersections. In [15], 343-355. Zbl0903.13003
22. [22] F. Diamond - The refined conjecture of Serre. In Elliptic curves, modular forms and Fermat's last theorem (Hong Kong, 1993). International Press, 1995, 22-37. Zbl0853.11031MR1363493
23. [23] F. Diamond - An extension of Wiles' results. In [15], 475-498. Zbl0917.11021MR1638490
24. [24] F. Diamond - On deformation rings and Hecke rings. Ann. Math.144 (1996), 137-166. Zbl0867.11032MR1405946
25. [25] F. Diamond - The Taylor-Wiles construction and multiplicity one. Invent. math.128 (1997), 379-391. Zbl0916.11037MR1440309
26. [26] F. Diamond, J. Im - Modular forms and modular curves. In "Seminar on Fermat's last theorem", Canadian Mathematical Society Conference Proceedings17, 1995 (V. Kumar Murty, editor). Zbl0853.11032MR1357209
27. [27] F. Diamond, R. Taylor - Lifting modular mod l representations. Duke Math. J.74 (1994), no. 2, 253-269. Zbl0809.11025MR1272977
28. [28] M. Dickinson - On the modularity of certain 2-adic Galois representations. Duke Math. J.109 (2001), no. 2, 319-382 Zbl1015.11020MR1845182
29. [29] S.J. Edixhoven - The weight in Serre's conjectures on modular forms. Invent. math?109 (1992), 563-594. Zbl0777.11013MR1176206
30. [30] J.-M. Fontaine - Groupes p-divisibles sur les corps locaux. Astérique47-48, S.M.F., 1977. Zbl0377.14009MR498610
31. [31] J.-M. Fontaine - Représentations p-adiques semi-stables. In "Périodes p-adiques," Astérisque223, S.M.F., 1994, p. 113-184. Zbl0865.14009MR1293972
32. [32] J.-M. Fontaine, B. Mazur - Geometric Galois representations. In "Elliptic curves, modular forms and Fermat's Last Theorem" (Hong Kong, 1993), International Press, 1995, pp. 41-78. Zbl0839.14011MR1363495
33. [33] K. Fujiwara - Deformation rings and Hecke rings in the totally real case. Preprint. 
34. [34] C. Khare - A local analysis of congruences in the (p,p)-case. II. Invent. Math.143 (2001), no. 1, 129-155. Zbl0971.11028MR1802794
35. [35] C. Khare - On isomorphisms between deformation and Hecke rings. Work in progress. 
36. [36] R.P. Langlands - Base change for GL(2). Ann. of Math. Studies96, Princeton University Press, Princeton, 1980. Zbl0444.22007MR574808
37. [37] J. Manoharmayum - Pairs of mod 3 and mod 5 representations arising from elliptic curves. Thesis, Cambridge University, 1998. MR1739229
38. [38] L. Moret-Bailly - Groupes de Picard et problèmes de Skolem II. Ann. Sci. ENS22 (1989), 181-194. Zbl0704.14015MR1005158
39. [39] R. Noot - Abelian varieties with l-adic Galois representation of Mumford's typeJ. Reine Angew. Math.519 (2000), 155-169 Zbl1042.14014MR1739726
40. [40] J. Oesterlé - Nouvelles approches du "théorème" de Fermat. Séminaire Bourbaki, 1987-88, exposé 694, Astérisque161-162, S.M.F. (1988), 175-186. Zbl0668.10024MR992208
41. [41] J. Oesterlé - Travaux de Wiles (et Taylor,...), partie II. Séminaire Bourbaki, 1994-95, exposé 804, Astérisque237, S.M.F. (1996), 333-355. Zbl0957.11028MR1423631
42. [42] R. Ramakrishna - On a variation of Mazur's deformation functor. Compositio Math.87 (1993), 269-286. Zbl0910.11023MR1227448
43. [43] R. Ramakrishna - Lifting Galois representations. Invent. math.138 (1999), 537-562. Zbl0968.11024MR1719819
44. [44] R. Ramakrishna - Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur. Preprint. Zbl1076.11035MR1935843
45. [45] K.A. Ribet, - On modular representations of Gal(Q/Q) arising from modular forms. Invent. math.100 (1990), 431-476. Zbl0773.11039MR1047143
46. [46] K. Rubin - Modularity of mod 5 representations. In [15], 463-474. Zbl0914.11030MR1638489
47. [47] T. Saito - Modular forms and p-adic Hodge theory. Invent. math.129 (1997), 607-620. Zbl0877.11034MR1465337
48. [48] J-P. Serre - Représentations l-adiques. Kyoto Int. Symposium on Algebraic Number Theory, Japan Soc. for the Promotion of Science (1977), pp. 177-193, (Oeuvres, t. III, pp. 384-400). Zbl0406.14015MR476753
49. [49] J-P. Serre — Sur les représentations modulaires de degré 2 de Gal(Q/Q). Duke Math. J.54 (1987), 179-230. Zbl0641.10026MR885783
50. [50] J-P. Serre - Travaux de Wiles (et Taylor,...), partie I. Séminaire Bourbaki, 1994-95, exposé 803, Astérisque237, S.M.F. (1996), 319-332. Zbl0957.11027MR1423630
51. [51] C. Skinner, A. Wiles - Residually reducible representations and modular forms. Pub. Math. IHES.89 (1999), 5-126. Zbl1005.11030MR1793414
52. [52] C. Skinner, A. Wiles - Base change and a problem of Serre. Duke Math. J.107 (2001), no. 1, 15-25. Zbl1016.11017MR1815248
53. [53] C. Skinner, A. Wiles - Nearly ordinary deformations of irreducible residual representations. Preprint. Zbl1024.11036
54. [54] N. Shepherd-Barron, R. Taylor - Mod 2 and mod 5 icosahedral representations. J. Amer. Math. Soc.10 (1997), 281-332. Zbl1015.11019MR1415322
55. [55] J. Tate - p-divisible groups. Proceedings of a conference on local fields (Driebergen, 1966), Springer, 1967, 158-183. Zbl0157.27601MR231827
56. [56] J. Tate - Number theoretic background. Proceedings of Symposia in Pure Mathematics33 (1979), part 2, 3-26. Zbl0422.12007MR546607
57. [57] R. Taylor - Icosahedral Galois representations. Pacific J. Math.: Special issue: Olga Taussky-Todd: in memoriam (1997), 337-347. Zbl0942.11031MR1610820
58. [58] R. Taylor - Remarks on a conjecture of Fontaine and Mazur. Preprint, http://www.math.harvard.edu/ MR1954941
59. [59] R. Taylor - On icosahedral Artin representations II. Preprint, http://www.math.harvard.edu/ Zbl1031.11031MR1981033
60. [60] R. Taylor, A. Wiles - Ring-theoretic properties of certain Hecke algebras. Ann. Math.141 (1995), 553-572. Zbl0823.11030MR1333036
61. [61] J. Tunnell - Artin's conjecture for representations of octahedral type. Bull. A.M.S.5 (1981), 173-175. Zbl0475.12016MR621884
62. [62] M. Volkov - Les représentations l-adiques associées aux courbes elliptiques sur Qp. J. Reine Angew. Math.535 (2001), 65-101. Zbl1024.11038MR1837096
63. [63] A. Weil - Exercices dyadiques. Invent. math.27 (1974), 1-22. Zbl0307.12017MR379445
64. [64] A. Wiles - Modular elliptic curves and Fermat's Last Theorem. Ann. Math.141 (1995), 443-551. Zbl0823.11029MR1333035

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