割圆域引论
2003-6
Springer Verlag
Lawrence C. Washington
487
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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. Also, Sinnott discovered a beautiful proof of the vanishing of Iwasawa's u-invariant that is much simpler than the one given in Chapter 7. Finally, Fermat's Last Theorem was proved by Wiles, using work of Frey, Ribet, Serre, Mazur, Langlands-Tunnell, Taylor-Wiles, and others. Although the proof, which is based on modular forms and elliptic curves, is much different from the cyclotomic approaches described in this book, several of the ingredients were inspired by ideas from cyclotomic fields and Iwasawa theory.
Preface to the Second Edition Preface to the First Edition CHAPTER 1 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 CHAPTER 7 Iwasawa's Construction of p-adic L-functionCHAPTER 8 Cyclotomic UnitsCHAPTER 9 The Second Case of Fermat's Last TheormCHAPTER 10 Galois Groups Acting on Ideal Class GroupsCHAPTER 11 Cyclotomic Fields of Class Number OneCHAPTER 12 Measures and DistributionCHAPTER 13 Iwasawa's Theory of Zp-extensionsCHAPTER 14 The Kronecker-Weber TheoremCHAPTER 15 The Main Conjecture and Annihilation of Class GroupsCHAPTER 16 MisscellanyAppendixTablesBibliographyList of SymbolsIndex
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虽然很厚，但是想要学就不要怕厚，要学CyclotomicFields，就要数Washington的这本书了