Résumé
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.
Contents- 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 Types
- Global Fields Of Finite Types
- On p-Class Groups And p-Class Field Towers
- The Cohomological Dimension Of GS
L'auteur - Helmut Koch
Koch, H., Humboldt-Universität zu Berlin, Germany
Caractéristiques techniques
PAPIER | |
Éditeur(s) | Springer |
Auteur(s) | Helmut Koch |
Parution | 21/08/2002 |
Nb. de pages | 190 |
Format | 16 x 24 |
Couverture | Broché |
Poids | 430g |
Intérieur | Noir et Blanc |
EAN13 | 9783540436294 |
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