描述
开 本: 16开纸 张: 胶版纸包 装: 平装是否套装: 否国际标准书号ISBN: 9787510070211
内容简介
奇尔德雷斯编著的《类域论》将Gauss、Legendre和其他的二次和更高阶的互反率巧妙结合，并将这些结果更加一般化，是学习类域理论的入门书籍。本书运用传统方法和原始技巧呈现书中的材料，思路清晰流畅，是这个领域的图书很难企及的。本书可以作为代数数论的研究生教程，尤其适合自学。书中有大量的练习贯穿始终，已经被证明了是一本很成功的教材。
目 录
1 A Brief Review 1 Number Fields 2 Completions of Number Fields 3 Some General Questions Motivating Class Field Theory2 Dirichlet's Theorem on Primes in Arithmetic Progressions 1 Characters of Finite Abelian Groups 2 Dirichlet Characters 3 Dirichlet Series 4 Dirichlet's Theorem on Primes in Arithmetic Progressions 5 Dirichlet Density3 Ray Class Groups 1 The Approximation Theorem and Infinite Primes 2 Ray Class Groups and the Universal Norm Index Inequality 3 The Main Theorems of Class Field Theory4 The Idelie Theory 1 Places of a Number Field 2 A Little Topology 3 The Group of Ide1es of a Number Field 4 Cohomology of Finite Cyclic Groups and the Herbrand Quotient 5 Cyclic Galois Action on Ideles5 Artin Reciprocity 1 The Conductor of an Abelian Extension of Number Fields and the Artin Symbol 2 Artin Reciprocity 3 An Example: Quadratic Reciprocity 4 Some Preliminary Results about the Artin Map on Local Fields6 The Existence Theorem, Consequences and Applications l The Ordering Theorem and the Reduction Lemma 2 Kummer n-extensions and the Proof of the Existence Theorem 3 The Artin Map on Local Fields 4 The Hilbert Class Field 5 Arbitrary Finite Extensions of Number Fields 6 Infinite Extensions and an Alternate Proof of the Existence Theorem. 7 An Example: Cyclotomic Fields7 Local Class Field Theory 1 Some Preliminary Facts About Local Fields 2 A Fundamental Exact Sequence 3 Local Units Modulo Norms 4 One-Dimensional Formal Group Laws 5 The Formal Group Laws of Lubin and Tare 6 Lubin-Tate Extensions 7 The Local Artin MapBibliographyIndex
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