# Modular Forms and Fermat's Last Theorem / Edition 1

ISBN-10: 0387989986

ISBN-13: 9780387989983

Pub. Date: 01/14/2000

Publisher: Springer New York

This volume contains expanded versions of lectures given at an instruc tional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's include The pu rpose 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)

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## Overview

This volume contains expanded versions of lectures given at an instruc tional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's include The pu rpose 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 Wile sF result can be combined with Ribet's theorem and ideas of Frey and S erre to show, at long last, that Fermat's Last Theorem is true.

## Product Details

ISBN-13:
9780387989983
Publisher:
Springer New York
Publication date:
01/14/2000
Edition description:
1st ed. 1997. 3rd printing 2000
Pages:
582
Product dimensions:
1.38(w) x 6.14(h) x 9.21(d)

I An Overview of the Proof of Fermat’s Last Theorem.- II A Survey of the Arithmetic Theory of Elliptic Curves.- III Modular Curves, Hecke Correspondences, and L-Functions.- IV Galois Coharnology.- V Finite Flat Group Schemes.- VI Three Lectures on the Modularity of

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and the Langlands Reciprocity Conjecture.- VII Serre’s Conjectures.- VIII An Introduction to the Deformation Theory of Galois Representations.- IX Explicit Construction of Universal Deformation Rings.- X Hecke Algebras and the Gorenstein Property.- XI Criteria for Complete Intersections.- XII—-adic Modular Deformations and Wiles’s “Main Conjecture”.- XIII The Flat Deformation Functor.- XIV Hecke Rings and Universal Deformation Rings.- XV Explicit Families of Elliptic Curves with Prescribed Mod NRepresentations.- XVI Modularity of Mod 5 Representations.- XVII An Extension of Wiles’ Results.- Appendix to Chapter XVII Classification of

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by the jInvariant of E.- XVIII Class Field Theory and the First Case of Fermat’s Last Theorem.- XIX Remarks on the History of Fermat’s Last Theorem 1844 to 1984.- XX On Ternary Equations of Fermat Type and Relations with Elliptic Curves.- XXI Wiles’ Theorem and the Arithmetic of Elliptic Curves.