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- [Browse]
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 Browse related items Request

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    Subject(s)
    Author
    Series
    Cambridge studies in advanced mathematics ; 165. [More in this series]
    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.
    ISBN
    • 9781107156371 (hardcover)
    • 1107156378 (hardcover)
    • 9781316609880
    • 131660988X
    LCCN
    2017024137
    OCLC
    989726707
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