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雷达卡
Authors: Helmut Koch
First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal p-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers.The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included.
Table of contents (14 chapters)
Front Matter
Introduction
Profinite Groups
Galois Theory of Infinite Algebraic Extensions
Cohomology of Profinite Groups
Free pro-p Groups
Cohomological Dimension
Presentation of pro-p Groups
Group Algebras of pro-p Groups
Results from Algebraic Number Theory
The Maximal p-Extension
Local Fields of Finite Type
Global Fields of Finite Type
On p-Class Groups and p-Class Field Towers
The Cohomological Dimension of Gs
Back Matter
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