割圆域导论

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《割圆域导论(第2版)(英文)》介绍了Since the publication of the first edition,several remarkable developments have taken place.The work of Thaine,Kolyvagin,and Rubin has produced fairly elementary proofs of Ribet's converse of Herbrand's theorem and of the Main Conjecture.The original proofs of both of these results used delicate techniques from algebraic geometry and were inaccessible to many readers.
书    名
割圆域导论
作    者
华盛顿 (Lawrence C.Washington)
出版日期
2014年7月1日
语    种
简体中文, 英语
ISBN
9787510077852
外文名
Introduction to Cyclotomic Fields
出版社
世界图书出版公司北京公司
页    数
487页
开    本
24
品    牌
世界图书出版公司北京公司

割圆域导论基本介绍

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割圆域导论内容简介

《割圆域导论(第2版)(英文)》由世界图书出版公司北京公司出版。

割圆域导论作者简介

作者:(美国)华盛顿(Lawrence C.Washington)

割圆域导论图书目录

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Preface to the Second Edition
  Preface to the First Edition
  CHAPTER Ⅰ
  Fermat's Last Theorem
  CHAPTER 2
  Basic Results
  CHAPTER 3
  Dirichlet Characters
  CHAPTER 4
  Dirichlet L-series and Class Number Formulas
  CHAPTER 5
  p-adic L-functions and Bernoulli Numbers
  5.1. p-adic functions
  5.2. p-adic L-functions
  5.3. Congruences
  5.4. The value at s -- 1
  5.5. The p-adic regulator
  5.6. Applications of the class number formula
  CHAPTER 6
  Stickelberger's Theorem
  6.1. Gauss sums
  6.2. Stickelberger's theorem
  6.3. Herbrand's theorem
  6.4. The index of the Stickelberger ideal
  6.5. Fermat's Last Theorem
  CHAPTER ?
  lwasawa's Construction of p-adic L-functions
  7.1. Group tings and power series
  7.2. p-adic L-functions
  7.3. Appfications
  7.4. Function fields
  7.5.
  CHAPTER 8
  Cyclotomic Units
  8.1. Cyclotomic units
  8.2. Proof of the p-adic class number formula
  8.3. Units of O(~,) and Vandiver's conjecture
  8.4. p-adic expansions
  CHAPTER 9
  The Second Case of Fermat's Last Theorem
  9.1. The basic argument
  9.2. The theorems
  CHAPTER 10
  Galois Groups Acting on Ideal Class Groups
  10.1. Some theorems on class groups
  10.2. Reflection theorems
  10.3. Consequences of Vandiver's conjecture
  CHAPTER I !
  Cyclotomic Fields of Class Number One
  11.1. The estimate for even characters
  11.2. The estimate for all characters
  ……
  CHAPTER 14
  CHAPTER 15
  The Main Conjecture and Annihilation of Class Groups
  CHAPTER 16
  Miscellany
  Appendix
  1. Inverse limits
  2. Infinite Galois theory and ramification theory
  3. Class field theory
  Tables
  1. Bernoulli numbers
  2. Irregular primes
  3. Relative class numbers
  4. Real class numbers
  Bibliography
  List of Symbols
  Index

  
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