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Modular Forms and Fermat’s Last Theorem

  • Gary Cornell
  • Joseph H. Silverman
  • Glenn Stevens
Book

Table of contents

  1. Front Matter
    Pages i-xix
  2. David E. Rohrlich, George F. Rohrlich
    Pages 41-100
  3. Lawrence C. Washington
    Pages 101-120
  4. John Tate
    Pages 121-154
  5. Bas Edixhoven
    Pages 209-242
  6. Bart de Smit, Hendrik W. Lenstra Jr.
    Pages 313-326
  7. Jacques Tilouine
    Pages 327-342
  8. Bart De Smit, Karl Rubin, René Schoof
    Pages 343-356
  9. Fred Diamond, Kenneth A. Ribet
    Pages 357-373
  10. Brian Conrad
    Pages 373-420
  11. Ehud De Shalit
    Pages 421-445
  12. Karl Rubin
    Pages 463-474
  13. Fred Diamond
    Pages 475-498
  14. H. W. Lenstra, P. Stevenhagen Jr.
    Pages 499-503
  15. Back Matter
    Pages 571-582

About this book

Introduction

This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.

Keywords

arithmetic deformation theory elliptic curve number theory

Editors and affiliations

  • Gary Cornell
    • 1
  • Joseph H. Silverman
    • 2
  • Glenn Stevens
    • 3
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA
  3. 3.Department of MathematicsBoston UniversityBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1974-3
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98998-3
  • Online ISBN 978-1-4612-1974-3
  • Buy this book on publisher's site
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