Article
MSC:
11D41,
11F80,
11G05,
11G18,
11G40,
14H52 | MR 1303554 | Zbl 0813.11016 | DOI: 10.21136/MB.1994.126199
Full entry |
PDF
(2.8 MB)
Feedback
PDF
(2.8 MB)
Feedback
Keywords:
modular curves; survey; Taniyama conjecture; Fermat’s last theorem
modular curves; survey; Taniyama conjecture; Fermat’s last theorem
References:
[1] S. Bloch K. Kato: L-functions and Tamagawa numbers of motives. In: The Grothendieck Festschrift I, Progress in Mathematics 86. Birkhäuser, Boston, Basel, Berlin, 1990, pp. 333-400. MR 1086888
[2] H. C. Clemens: A scrapbook of complex curve theory. Plenum Press, New York, London, 1980. MR 0614289 | Zbl 0456.14016
[3] J. Coates A. Wiles: On the Conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977), 223-251. DOI 10.1007/BF01402975 | MR 0463176
[4] M. Eichler: Quaternare quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion. Arch. Math. 5 (1954), 355-366. DOI 10.1007/BF01898377 | MR 0063406
[5] G. Faltings: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math. 73 (1983), 349-366. DOI 10.1007/BF01388432 | MR 0718935 | Zbl 0588.14026
[6] M. Flach: A finiteness theorem for the symmetric square of an elliptic curve. Invent. Math. 109 (1992), 307-327. DOI 10.1007/BF01232029 | MR 1172693 | Zbl 0781.14022
[7] G. Frey: Links between stable elliptic curves and certain diophantine equations. Ann. Univ. Sarav. 1 (1986), 1-40. MR 0853387 | Zbl 0586.10010
[8] G. Frey: Links between solutions of A - B = C and elliptic curves. Lecture Notes in Math. 1380. 1989, pp. 31-62. DOI 10.1007/BFb0086544 | MR 1009792 | Zbl 0688.14018
[9] P. Griffiths J. Harris: Principles of Algebraic Geometry. Wiley, New York, 1978. MR 0507725
[10] H. Hasse: Beweis des Analogons der Riemannschen Vermutung für die Artinschen und F.K. Schmidtschen Kongruenzzetafunktionen in gewissen elliptischen Fallen. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. (1933), 253-262.
[11] K. Ireland M. Rosen: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics 84, Springer, New York, Heidelberg, Berlin, 1982. MR 0661047
[12] V. A. Kolyvagin: Koněčnosť E(Q) i Ш(E, Q) dlja podklassa krivych Vejlja. Izv. Akad. Nauk SSSR, Ser. Mat. 52 (1988), 522-540.
[13] V. A. Kolyvagin: O gruppach Mordella-Vejlja i Šafareviča-Tejta dlja elliptičeskich krivych Vejlja. zv. Akad. Nauk SSSR, Ser. Mat. 52(1988), 1156-1180.
[14] V. A. Kolyvagin: Euler Systems. In: The Grothendieck Festschrift II, Progress in Mathematics 87. Birkhäuser, Boston, Basel, Berlin, 1990, pp. 435-483. MR 1106906 | Zbl 0742.14017
[15] S. Lang: Elliptic Functions. Addison-Wesley, Reading, Mass., 1973. MR 0409362 | Zbl 0316.14001
[16] S. Lang: Introduction to Modular Forms. Springer, Berlin, Heidelberg, New York, 1976. MR 0429740 | Zbl 0344.10011
[17] B. Mazur: Modular curves and the Eisenstein ideal. Publ. Math. IHES 47 (1977), 33-186. DOI 10.1007/BF02684339 | MR 0488287 | Zbl 0394.14008
[18] B. Mazur: Deforming Galois representations. Galois Groups over Q. Math. Sci. Res. Inst. Publ., vol. 16. Springer-Verlag Berlin and New York, 1989, pp. 385-437. DOI 10.1007/978-1-4613-9649-9_7 | MR 1012172
[19] B. Mazur: Letter to J.-F. Mestre (16 August 1985). Zbl 0588.76163
[20] B. Mazur: Number theory as gadfly. Amer. Math. Monthly 98 (1991), 593-610. DOI 10.1080/00029890.1991.11995762 | MR 1121312 | Zbl 0764.11021
[21] B. Mazur: On the passage from local to global in number theory. Bulletin AMS 29 (1993), no. 1, 14-50. DOI 10.1090/S0273-0979-1993-00414-2 | MR 1202293 | Zbl 0813.14016
[22] B. Mazur K. Ribet: Two-dimensional representations in the arithmetic of modular curves. In: Asterisque 196/197, S.M.F.. 1991, pp. 215-255. MR 1141460
[23] B. Mazur A. Wiles: Class fields of abelian extensions of Q. Invent. Math. 76(1984), 179-330. MR 0742853
[24] J. Nekovář: Values of L-functions and p-adic cohomology. In: Proceedings ECM 1992 Paris, to appear. MR 1341847
[25] A. Ogg: Modular forms and Dirichlet series. Benjamin, 1969. MR 0256993 | Zbl 0191.38101
[26] K. A. Ribet: On modular representations of $Gal(\overline{Q}/Q)$ arising from modular forms. Invent. Math. 100 (1990), 431-476. DOI 10.1007/BF01231195 | MR 1047143
[27] K. A. Ribet: From the Taniyama-Shimura Conjecture to Fermat's Last Theorem. Ann. Fac. Sci. Toulouse Math. 11 (1990), 116-139. DOI 10.5802/afst.698 | MR 1191476 | Zbl 0726.14015
[28] K. A. Ribet: Report on mod l representations of $Gal(\overline{Q}/Q)$. In: Proceedings of the "Motives" conference, Seattle 1991. to appear in Proc. Symp. Pure Math. MR 1265566
[29] K. Rubin: The "main conjecture" of Iwasawa theory for imaginary quadratic fields. Invent. Math. 103 (1991), 25-68. DOI 10.1007/BF01239508 | MR 1079839
[30] J.-P. Serre: A Course in Arithmetic. Springer, New York, 1973. MR 0344216 | Zbl 0256.12001
[31] J.-P. Serre: Lettre à J.-F. Mestre, (13 Août 1985). Contemp. Math. 67(1987), 263-268. MR 0902597 | Zbl 0596.12004
[32] J.-P. Serre: Sur les représentations modulaires de degré 2 de Gal. Duke Math. J. 54 (1987), 179-230. DOI 10.1215/S0012-7094-87-05413-5 | MR 0885783
[33] G. Shimura: Correspondences modulaires et les fonctions $\zeta$ de courbes algébriques. J. Math. Soc. Japan 10 (1958), 1-28. DOI 10.2969/jmsj/01010001 | MR 0095173
[34] G. Shimura: Introduction to the Arithmetic Theory of Automorphic Functions. Princeton University Press, 1971. MR 0314766 | Zbl 0221.10029
[35] J. H. Silverman: The arithmetic of elliptic curves. Graduate Texts in Math., vol. 106, Springer, New York, 1986, MR 0817210 | Zbl 0585.14026
[36] J. Tunnell: Artin's conjecture for representations of octahedral type. Bull. Amer. Math. Soc. (N.S.) 5 (1981), 173-175. DOI 10.1090/S0273-0979-1981-14936-3 | MR 0621884 | Zbl 0475.12016
[37] H. Weber: Lehrbuch der Algebra, III. 1908.
[38] A. Weil: Elliptic functions according to Eisenstein and Kronecker. Springer, New York, 1976. MR 0562289 | Zbl 0318.33004
[39] A. Wiles: Higher explicit reciprocity laws. Ann. of Math. 107(1978), 235-254. DOI 10.2307/1971143 | MR 0480442 | Zbl 0378.12006
[40] A. Wiles: On ordinary $\lambda$-adic representations associated to modular forms. Invent. Math. 94 (1988), 529-573. DOI 10.1007/BF01394275 | MR 0969243 | Zbl 0664.10013
[41] A. Wiles: The Iwasawa conjecture for totally real fields. Ann. of Math. 131 (1990), 493-540. DOI 10.2307/1971468 | MR 1053488 | Zbl 0719.11071
[42] A. Wiles: On a conjecture of Brumer. Ann. of Math. 131 (1990), 555-565. DOI 10.2307/1971470 | MR 1053490 | Zbl 0719.11082
Search
Partner of
