Cohomology of number fields /

Cohomology of number fields /

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Bibliographic Details
Author / Creator:	Neukirch, Jürgen, 1937-, author.
Edition:	Second edition, Correct second printing.
Imprint:	Berlin : Springer, [2008] ©2008
Description:	1 online resource (xv, 825 pages) : illustrations.
Language:	English
Series:	Grundlehren der mathematischen Wissenschaften ; 323 Grundlehren der mathematischen Wissenschaften ; 323.
Subject:	Algebraic fields. Galois theory. Homology theory. Algebraic fields. Galois theory. Homology theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/9804083

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Other authors / contributors:	Schmidt, Alexander, 1965-, author. Wingberg, Kay, author.
ISBN:	9783540378891 (electronic bk.) 3540378898 (electronic bk.) 354037888X 9783540378884
Notes:	Includes bibliographical references (pages [805]-819) and index. Description based on print version record.
Summary:	The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramification, Poitou-Tate duality, Hasse principles, theorem of Grunwald-Wang, Leopoldts conjecture, Riemanns existence theorem, the theorems of Iwasawa and of afarevic on solvable groups as Galois groups, Iwasawa theory, and anabelian principles. New material is introduced here on duality theorems for unramified and tamely ramified extensions, a careful analysis of 2-extensions of real number fields and a complete proof of Neukirchs theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008 edition.
Other form:	Print version: Neukirch, Jürgen, 1937- Cohomology of number fields. Second edition 354037888X

Table of Contents:

Part I Algebraic Theory: Cohomology of Profinite Groups
Some Homological Algebra
Duality Properties of Profinite Groups
Free Products of Profinite Groups
Iwasawa Modules
Part II Arithmetic Theory: Galois Cohomology
Cohomology of Local Fields
Cohomology of Global Fields
The Absolute Galois Group of a Global Field
Restricted Ramification
Iwasawa Theory of Number Fields
Anabelian Geometry
Literature
Index.