TY  - BOOK
AU  - Gille,Philippe
AU  - Szamuely,Tamás
TI  - Central simple algebras and Galois cohomology
T2  - Cambridge studies in advanced mathematics
SN  - 9781316661277 (ebook)
AV  - QA612.3 .G55 2017
U1  - 512/.32 23
PY  - 2017///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Galois cohomology
KW  - Algebra
KW  - Associative algebras
KW  - Algebra, Homological
N1  - Title from publisher's bibliographic system (viewed on 28 Aug 2017)
N2  - 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
UR  - https://doi.org/10.1017/9781316661277
ER  -