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Central simple algebras and Galois cohomology / Phillipe Gille, Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordon, Lyon ; Tamás Szamuely, Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest.
Author
Gille, Philippe, 1968-
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Format
Book
Language
English
Εdition
Second edition.
Published/Created
Cambridge ; New York, NY : Cambridge University Press, 2017.
©2017
Description
xi, 417 pages ; 24 cm.
Availability
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA612.3 .G55 2017
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Details
Subject(s)
Galois cohomology
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Algebra
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Associative algebras
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Algebra, Homological
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Author
Szamuely, Tamás
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Series
Cambridge studies in advanced mathematics ; 165.
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Summary note
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.
Notes
First edition published 2006.
Bibliographic references
Includes bibliographical references and index.
Contents
Quaternion algebras
Central simple algebras and Galois descent
Techniques from group cohomology
The cohomological Brauer group
Severi-Brauer varieties
Residue maps
Milnor K-theory
The Merkurjev-Suslin theorem
Symbols in positive characteristic
Appendix: a breviary of algebraic geometry.
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ISBN
9781107156371 (hardcover)
1107156378 (hardcover)
9781316609880
131660988X
LCCN
2017024137
OCLC
989726707
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