Modular Forms and Fermat's Last Theorem
Modular Forms and Fermat's Last Theorem
复制标题
模形式和费马大定理
DOI：
10.1007/978-1-4612-1974-3
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
G. Stevens
中科院分区：
文献类型：
--
作者：
G. Cornell;J. Silverman;G. Stevens
这卷包含了扩大讲座在会议上提出的一些理论和算术几何在波士顿大学举行。介绍和解释怀尔斯的许多思想和技巧，并说明如何将他的结果与里贝茨定理以及Frey和Serre的思想结合起来证明费马大定理。这本书首先概述了完整的证明，其次是几个介绍性的章节调查的基本理论椭圆曲线，模函数和曲线，伽罗瓦上同调，有限群计划。表示论是证明的核心，在自守表示和朗兰兹-通内尔定理的一章中进行了讨论，随后深入讨论了Serres代数、伽罗瓦变形、通用变形环、Hecke代数和完全相交。这本书的结论是向前看和向后看，反映了历史的问题，同时把怀尔斯定理到一个更一般的丢番图的背景下，建议未来的应用。学生和专业数学家都将发现这是一个不可或缺的资源。
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, 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 an indispensable resource.