Elliptic curves, modular forms, & Fermat’s last theorem. Proceedings ot the conference on elliptic curves and modular forms held at the Chinese University of Hong Kong, December 18-21, 1993. (English) Zbl 0824.00025

Series in Number Theory. 1. Cambridge, MA: International Press. 191 p. (1995).

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The articles of this volume will be reviewed individually.
From the Preface (by John Coates and Shing-Tung Yau): The impetus for organizing the conference arose from Andrew Wiles’ deep and spectacular work on the celebrated conjecture that every elliptic curve over \(\mathbb{Q}\) is modular. ... It is now history that Wiles himself, assisted by R. Taylor, found a beautiful proof of the desired upper bound. As a result we now know today the remarkable fact that every semi-stable elliptic curve over \(\mathbb{Q}\) is modular. Not only this result is revolutionary in its own right for the study of the arithmetic of these elliptic curves, but it has the added bonus that it provides at last a proof of Fermat’s Last Theorem, thanks to the earlier works of Frey, Ribet and others. [ For the reviews of G. Faltings on the papers by Wiles and Taylor-Wiles, Ann. Math., II. Ser. 141, No. 3, 443-551, 553-572 (1995) see Zbl 0823.11029 and 823.11030.]
The present volume is a mixture of the texts of some lectures, together with a number of recent articles related to the general theme of the conference.
Indexed articles:
Coates, J.; Sydenham, A., On the symmetric square of a modular elliptic curve, 2-21 [Zbl 0943.11032]
Diamond, Fred, The refined conjecture of Serre, 22-37 [Zbl 0853.11031]
Elkies, Noam D., Wiles minus epsilon implies Fermat, 38-40 [Zbl 0836.11013]
Fontaine, Jean-Marc; Mazur, Barry, Geometric Galois representations, 41-78 [Zbl 0839.14011]
Frey, Gerhard, On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2, 79-98 [Zbl 0856.11026]
Lenstra, H. W. jun., Complete intersections and Gorenstein rings, 99-109 [Zbl 0860.13012]
Merel, Loïc, Homology of affine modular curves and modular parametrization, 110-130 [Zbl 0845.11023]
Ribet, Kenneth A., Irreducible Galois representations arising from component groups of Jacobians, 131-147 [Zbl 0976.11028]
Rubin, K.; Silverberg, A., Families of elliptic curves with constant \(\text{mod }p\) representations, 148-161 [Zbl 0856.11027]
Tate, John, A review of non-Archimedean elliptic functions., 162-184 [Zbl 1071.11508]
Taylor, Richard, On Galois representations associated to Hilbert modular forms. II, 185-191 [Zbl 0836.11017]


00B25 Proceedings of conferences of miscellaneous specific interest
11-06 Proceedings, conferences, collections, etc. pertaining to number theory
14-06 Proceedings, conferences, collections, etc. pertaining to algebraic geometry


Zbl 0823.11029