Galois cohomology伽罗瓦上同调

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作者： Jean-Pierre Serre著

出版社：湖南文艺出版社

出版时间： 2001-11-1字数：版次： 1页数： 207印刷时间： 2001/11/01开本： 16开印次： 1纸张：胶版纸I S B N ： 9783540421924包装：精装内容简介

This is an updated English translation of "Cohomologie Galoisienne", published more than 30 years ago as one of the very first Lecture Notes in Mathematics (LNM 5). It includes a reproduction of an influential paper of R. Steinberg, together with some new material and an expanded bibliography.

Foreword

Chapter I Cohomology of profinite groups

1 Profinite groups

2 Cohomology

3 Cohomological dimension

4 Cohomology of pro-p-groups

5 Nonabelian cohomology

Bibliography remarks for Chapter I

Appendix 1 J. Tate - Some duality theorems

Appendix 2 The Golod-Shafarevich inequality

Chapter II Galois cohomology, the commutative case

1 Generalities

2 Criteria for cohomological dimension

3 Fields of dimension [less than or equal to]1

4 Transition theorems

5 p-adic fields

6 Algebraic number fields

Bibliographic remarks for Chapter II

Appendix Galois cohomology of purely transcendental extensions

Chapter III Nonabelian Galois cohomology

1 Forms

2 Fields of dimension [less than or equal to]1

3 Fields of dimension [less than or equal to]2

4 Finiteness theorems

Bibliographic remarks for Chapter III

Appendix 1 Regular elements of semisimple groups

Appendix 2 Complements on Galois cohomology

Bibliography

Index