Overview

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 idele and the idele class groups, Poitou-Tate duality for finitely generated Galois modules, the Hasse principle, the theorem of Grundwald-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.

Full Product Details

Author:   Jurgen Neukirch ,  Alexander Schmidt ,  Kay Wingberg
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   v. 323
ISBN:  

9783540666714

ISBN 10:   3540666710
Pages:   714
Publication Date:   December 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Replaced By:   9783540378884
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

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