Item description for Cohomology of Number Fields (Grundlehren der mathematischen Wissenschaften) (Grundlehren der mathematischen Wissenschaften) by Jürgen Neukirch...
The present 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, Leopoldt s conjecture, Riemann s 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 Neukirch s theorem on solvable Galois groups with given local conditions.
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Est. Packaging Dimensions: Length: 9.3" Width: 6.4" Height: 1.4" Weight: 2.4 lbs.
Release Date Mar 27, 2008
ISBN 354037888X ISBN13 9783540378884