Galois Theory of p-Extensions
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Author
Publication
2002 - Springer Berlin Heidelberg, Berlin, Heidelberg, Germany
Language
English
Word Count
47,750 words, Guess
Page Count
191 pages
Physical Format
[electronic resource] /
Identifiers
- Open LibraryOL27040605M
- ISBN-139783642078170
- ISBN-103642078176
- OCLC Control Number851391164
- OCLC Control Numbergaloistheoryemcl00koch
Classifications
- DDC512.66
- LCCQA612.33
Description
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.
Subjects
Series Statement
- Springer Monographs in Mathematics
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