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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.

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前言/序言

割圆域导论（第2版） 电子书 下载 mobi epub pdf txt

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Introduction to Cyclotomic Fields

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非常好的书籍，值得推荐。

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现代数论方面的专著！

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数论方面的书

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好

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Introduction to Cyclotomic Fields

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Introduction to Cyclotomic Fields

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割圆域一般称为分圆域，相关的知识是数论方向的数学家必须学习了解的。分圆域可以用来解决很多数论的经典难题。本书第一版之后，有好几个重大的进展，Herbrand 的定理出现了初等证明，最初的证明是依赖代数几何。本书作者 Lawrence 写了好几本数论的书，都受到好评。相信本书，是著名的GTM 中的一本，也不会让读者失望。

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非常好的书籍，值得推荐。

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