本书是Boston大学举办的数论和代数会议的讲义扩张而成。书中介绍和扩充讲述了Wiles的许多观点和技巧，并阐述了他的结果是如何与Ribets定理、Frey，Serre思想的结合，来证明费马最后定理。从一个完整的证明开始，紧接着用一些章节介绍了双曲线、模函数、曲线、伽罗瓦上同调和有限群的基本概念。表示理论是整个证明的核心，在一章有关自同构表示论和Langlands-Tunnell定理给出，紧随其后深度介绍Serres猜想、伽罗瓦变形、一般变形环、Hacke代数。本书以回顾和展望作为结束，既反映了这个问题的历史，又将Wiles定理放在了一个更加一般的Diophantine背景，给出了预期应用。数学专业的学生和老师将会发现这本书是一部很难得参考书。

Preface
Contributors
Schedule of Lectures
Introduction


CHAPTER Ⅰ
An Overview of the Proof of Fermat's Last Theorem GLENN STEVENS
A remarkable elliptic curve
Galois representations
A remarkable Galois representation
Modular Galois representations
The Modularity Conjecture and Wiles's Theorem
The proof of Fermat's Last Theorem
The proof of Wiles's Theorem
References


CHAPTER Ⅱ
A Survey of the Arithmetic Theory of Elliptic Curves JOSEPH H. SILVERMAN
Basic definitions
The group law
Singular cubics
Isogenies
The endomorphism ring
Torsion points
Galois representations attached to E
The Weil pairing
Elliptic curves over finite fields
Elliptic curves over C and elliptic functions
The formal group of an elliptic curve
Elliptic curves over local fields
The Selmer and Shafarevich-Tate groups
Discriminants, conductors, and L-series
Duality theory
Rational torsion and the image of Galois
Tate curves
Heights and descent
The conjecture of Birch and Swinnerton-Dyer
Complex multiplication
Integral points
References


CHAPTER Ⅲ
Modular Curvcs, Hecke Correspondences, and L-Functions DAVID E.ROHRLICH
Modular curves
The Hcckc corrospondences
L-functions
Rcfcrcnccs


CHAPTER Ⅳ
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