类域论

本书特色

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    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。

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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

封面

书名:类域论

作者:奇尔德雷斯

页数:226

定价:¥39.0

出版社:世界图书出版公司

出版日期:2014-03-01

ISBN:9787510070211

PDF电子书大小:101MB 高清扫描完整版