Cohomology of Number Fields. Second Edition

種類:

電子ブック

責任表示:

by Jürgen Neukirch, Alexander Schmidt, Kay Wingberg

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2008

著者名:

• Neukirch, Jürgen
• Schmidt, Alexander
• Wingberg, Kay
• SpringerLink (Online service)

シリーズ名:

Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 323

ISBN:

9783540378891 [3540378898]    

注記:

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, Leopoldt’s conjecture, Riemann’s existence theorem, the theorems of Iwasawa and of Šafarevic 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 Neuk

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