Cohomology of Number Fields
This 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. In all it is a virtually complete treatment of a vast array of central topics in algebraic number...
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| Main Authors: | , , |
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| Format: | Book/Monograph |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer
2008
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| Edition: | Second Edition |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
323 SpringerLink Bücher Springer eBook Collection Mathematics and Statistics |
| DOI: | 10.1007/978-3-540-37889-1 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/978-3-540-37889-1 Verlag, Inhaltsverzeichnis: http://d-nb.info/980792630/04 Verlag, Zentralblatt MATH, Inhaltstext: https://zbmath.org/?q=an:1136.11001 
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| Author Notes: | by Jürgen Neukirch, Alexander Schmidt, Kay Wingberg |
| Summary: | This 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. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields. 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 Neukirch’s theorem on solvable Galois groups with given local conditions. The present edition is a corrected printing of the 2008 edition |
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| Physical Description: | Online Resource |
| ISBN: | 9783540378891 |
| DOI: | 10.1007/978-3-540-37889-1 |