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＜E-Book＞
Galois Theory of p-Extensions / by Helmut Koch
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2002.
Publisher	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Year	2002
Language	English
Size	XIII, 191 p : online resource
Authors	*Koch, Helmut author SpringerLink (Online service)
Subjects	LCSH:K-theory LCSH:Group theory FREE:K-Theory FREE:Group Theory and Generalizations
Notes	1. Profinite Groups -- 2. Galois Theory of Infinite Algebraic Extensions -- 3. Cohomology of Profinite Groups -- 4. Free pro-p Groups -- 5. Cohomological Dimension -- 6. Presentation of pro-p Groups -- 7. Group Algebras of pro-p Groups -- 8. Results from Algebraic Number Theory -- 9. The Maximal p-Extension -- 10. Local Fields of Finite Type -- 11. Global Fields of Finite Type -- 12. On p-Class Groups and p-Class Field Towers -- 13. The Cohomological Dimension of GS -- References -- Notation -- Postscript -- Additional References -- Author Index 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 HTTP:URL=https://doi.org/10.1007/978-3-662-04967-9

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