作者：康奈尔
页数：582
出版社：世界图书出版公司
出版日期：2014
ISBN：9787510070174
电子书格式：pdf/epub/txt
内容简介
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。
作者简介
Gary Cornell, Joseph H. Silverman, Glenn Stevens是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
康奈尔编著的《模形式与费马大定理》内容介绍 ：this volume is the record of an instructional conference on number theory and arithmetic geometry held from august 9 through 18, 1995 at boston university. it contains expanded versions of all of the major lectures given during the conference. we want to thank all of the speakers, all of the writers whose contributions make up this volume, and all of the “behind-the-scenes” folks whose assistance was indispensable in running the con-ference. we would especially like to express our appreciation to patricia pacelli, who coordinated most of the details of the conference while in the midst of writing her phd thesis, to jaap top and jerry tunnell, who stepped into the breach on short notice when two of the invited speakers were unavoidably unable to attend, and to stephen gelbart, whose courage and enthusiasm in the face of adversity has been an inspiration to us.
目录
contributors
schedule of lectures
introduction
chapter ⅰ
an overview of the proof of fermat’s last theorem
glenn stevens
1. a remarkable elliptic curve
2. galois representations
3. a remarkable galois representation
4. modular galois representations
5. the modularity conjecture and wiles’s theorem
6. the proof of fermat’s last theorem
7. the proof of wiles’s theorem
references
chapter ⅱ
a survey of the arithmetic theory of elliptic curves
joseph h. silverman
1. basic definitions
2. the group law
3. singular cubics
4. isogenies
5. the endomorphism ring
6. torsion points
7. galois representations attached to e
8. the well pairing
9. elliptic curves over finite fields
10. elliptic curves over c and elliptic functions
11. the formal group of an elliptic curve
12. elliptic curves over local fields
13. the selmer and shafarevich-tate groups
14. discriminants, conductors, and l-series
15. duality theory
16. rational torsion and the image of galois
17. tate curves
18. heights and descent
19. the conjecture of birch and swinnerton-dyer
20. complex multiplication
21. integral points
references
chapter ⅲ
modular curves, hecke correspondences, and l-functions
david e. rohrlich
chapter ⅳ
galois cohomology
lawrence c. washington
chapter ⅴ
finite flat group schemes
john tate
chapter ⅵ
three lectures on the modularity of pr,3 and the langlands reciprocity conjecture
stephen gelhart
chapter ⅶ
serre’s conjectures
bas edixhoven
chapter ⅷ
an introduction to the deformation theory of galois representations
barry mazur
chapter ⅸ
explicit construction of universal deformation rings
bart de smit and hendrik w. lenstra, jr.
chapter ⅹ
hecke algebras and the gorenstein property
acques tilouine
chapter ?
criteria for complete intersections
bart de smit, karl rubin, and rene schoof
chapter ?
l-adic modular deformations and wiles’s “main conjecture”
fred diamond and kenneth a. ribet
chapter ?ⅰ
the flat deformation functor
brian conrad
chapter ⅹⅳ
hecke rings and universal deformation rings
ehud de shalit
chapter ⅹⅴ
explicit families of elliptic curves
with prescribed mod n representations
alice silverberg
chapter ⅹⅵ
modularity of mod 5 representations
karl rubin
chapter ⅹⅶ
an extension of wiles’ results
fred diamond
appendix to chapter ⅹⅶ
classification of ρe,l by the j invariant of e
fred diamond and kenneth kramer
chapter ⅹⅷ
class field theory and the first case of fermat’s last theorem
hendrik w. lenstra, jr. and peter stevenhagen
chapter ?ⅹ
remarks on the history of fermat’s last theorem 1844 to 1984
michael rosen
introduction
appendix a: kummer congruence and hilbert’s theorem
bibliography
