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Seminar on Fermat's Last Theorem
Edited by: V. Kumar Murty, University of Toronto, ON, Canada
A co-publication of the AMS and Canadian Mathematical Society.
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Conference Proceedings, Canadian Mathematical Society
1995; 265 pp; softcover
Volume: 17
Reprint/Revision History:
reprinted 1996
ISBN-10: 0-8218-0313-1
ISBN-13: 978-0-8218-0313-4
List Price: US$60
Member Price: US$48
Order Code: CMSAMS/17
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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 1993-1994 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 Taylor-Wiles 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: Shimura-Taniyama-Weil 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
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