Cohomology of Number Fields (Grundlehren der mathematischen Wissenschaften)

Neukirch, Jürgen

ISBN 10: 3540666710 / ISBN 13: 9783540666714

Published by Springer, 2000

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Synopsis:

Galois modules over local and global fields form the main subject of this monograph, which can serve both as a textbook for students, and as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides the necessary algebraic background. The arithmetic part deals with Galois groups of local and global fields: local Tate duality, the structure of the absolute Galois group of a local field, extensions of global fields with restricted ramification, cohomology of the idèle and the idèle class groups, Poitou-Tate duality for finitely generated Galois modules, the Hasse principle, the theorem of Grunwald-Wang, Leopoldt's conjecture, Riemann's existence theorem for number fields, embedding problems, the theorems of Iwasawa and of Safarevic on solvable groups as Galois groups over global fields, Iwasawa theory of local and global number fields, and the characterization of number fields by their absolute Galois groups.

Bibliographic Details

Title: Cohomology of Number Fields (Grundlehren der...
Publisher: Springer
Publication Date: 2000
Binding: Paperback
Condition: new