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Central simple algebras and Galois c...

Gille, Philippe, (1968-)

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Central simple algebras and Galois cohomology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Central simple algebras and Galois cohomology/ Philippe Gille, Tamas Szamuely.
作者:	Gille, Philippe,
其他作者:	Szamuely, Tamas.
出版者:	Cambridge :Cambridge University Press, : 2017.,
面頁冊數:	xi, 417 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 28 Aug 2017).
標題:	Galois cohomology. -
電子資源:	https://doi.org/10.1017/9781316661277
ISBN:	9781316661277

Central simple algebras and Galois cohomology
Gille, Philippe,1968-

Central simple algebras and Galois cohomology[electronic resource] /Philippe Gille, Tamas Szamuely. - Second edition. - Cambridge :Cambridge University Press,2017. - xi, 417 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;165. - Cambridge studies in advanced mathematics ;165..

Title from publisher's bibliographic system (viewed on 28 Aug 2017).

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.

ISBN: 9781316661277Subjects--Topical Terms:

888612
Galois cohomology.

LC Class. No.: QA612.3 / .G55 2017

Dewey Class. No.: 512.32

Central simple algebras and Galois cohomology
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500 $a Title from publisher's bibliographic system (viewed on 28 Aug 2017).
520 $a 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.
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