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.

Format:

Book

Author/Creator:

Gille, Philippe, 1968- author.

Szamuely, Tamás, author.

Series:

Cambridge studies in advanced mathematics ; 165.

Cambridge studies in advanced mathematics ; 165

Language:

English

Subjects (All):

Galois cohomology.

Algebra.

Associative algebras.

Algebra, Homological.

Physical Description:

xi, 417 pages ; 24 cm.

Edition:

Second edition.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2017.

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.

Notes:

Includes bibliographical references and index.

ISBN:

9781107156371

1107156378

OCLC:

989726707