The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting poin...

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Bibliographic Details

Main Author:	Gille, Philippe 1968- (Author)
Format:	Electronic eBook
Language:	English
Published:	Cambridge Cambridge University Press 2017
Edition:	Second edition
Series:	Cambridge studies in advanced mathematics 165
Subjects:	Galois cohomology Algebra Associative algebras Algebra, Homological Zentral einfache Algebra Galois-Kohomologie
Online Access:	BSB01 FHN01 Volltext
Summary:	The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev–Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi–Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev–Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch–Gabber–Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics
Item Description:	Title from publisher's bibliographic system (viewed on 28 Aug 2017)
Physical Description:	1 online resource (xi, 417 pages)
ISBN:	9781316661277
DOI:	10.1017/9781316661277