Conference Proceedings, Canadian Mathematical Society 1995; 265 pp; softcover Volume: 17 Reprint/Revision History: reprinted 1996 ISBN10: 0821803131 ISBN13: 9780821803134 List Price: US$60 Member Price: US$48 Order Code: CMSAMS/17
 The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his work establishes a new reciprocity law. Reciprocity laws lie at the heart of number theory. Wiles' work draws on many of the tools of modern number theory and the purpose of this volume is to introduce readers to some of this background material. Based on a seminar held during 19931994 at the Fields Institute for Research in Mathematical Sciences, this book contains articles on elliptic curves, modular forms and modular curves, Serre's conjectures, Ribet's theorem, deformations of Galois representations, Euler systems, and annihilators of Selmer groups. All of the authors are well known in their field and have made significant contributions to the general area of elliptic curves, Galois representations, and modular forms. Features:  Brings together a unique collection of number theoretic tools.
 Makes accessible the tools needed to understand one of the biggest breakthroughs in mathematics.
 Provides numerous references for further study.
Titles in this series are copublished with the Canadian Mathematical Society. Members of the Canadian Mathematical Society may order at the AMS member price. Readership Advanced graduate students and researchers studying the recent developments on modular elliptic curves, and Fermat's Last Theorem. Reviews "Anyone who wants to study the proof of Wiles and TaylorWiles will find these proceedings valuable and helpful."  Monatshefte für Mathematik Table of Contents  V. K. Murty  Modular elliptic curves
 F. Diamond and J. Im  Modular forms and modular curves
 H. Darmon  Serre's conjectures
 D. Prasad  Ribet's theorem: ShimuraTaniyamaWeil implies Fermat
 F. Q. Gouvêa  Deforming Galois representations: a survey
 F. Destrempes  Deformations of Galois representations: the flat case
 V. A. Kolyvagin  Bounding Selmer groups via the theory of Euler systems
 M. Flach  Annihilation of Selmer groups for the adjoint representation of a modular form
