Galois Theory of p-Extensions

2002
ISBN: 978-3-540-43629-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 191 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1050 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Koch, Helmut

Weitere Mitwirkende

Lemmermeyer, F.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.