Cohomology of Number Fields [electronic resource] /by Jürgen Neukirch, Alexander Schmidt, Kay Wingberg.
by Neukirch, Jürgen [author.]; Schmidt, Alexander [author.]; Wingberg, Kay [author.]; SpringerLink (Online service).
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BookSeries: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics: 323Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : 2008.Edition: Second Edition.Description: XV, 826 p. online resource.ISBN: 9783540378891.Subject(s): Mathematics | Geometry, algebraic | Group theory | Number theory | Mathematics | Number Theory | Algebraic Geometry | Group Theory and GeneralizationsDDC classification: 512.7 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
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| MAIN LIBRARY | QA241-247.5 (Browse shelf) | Available |
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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.
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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