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This book is the first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields. Starting from the basics, it reaches such advanced results as the Merkurjev-Suslin theorem. This theorem is both the 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, but no homological algebra, the book covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, residue maps and, finally, Milnor K-theory and K-cohomology. The last chapter rounds off the theory by presenting the results in positive characteristic, including the theorem of Bloch-Gabber-Kato. The book is suitable as a textbook for graduate students and as a reference for researchers working in algebra, algebraic geometry or K-theory.

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Book Details

ISBN: 9780521861038
ISBN-10: 0521861039
Format: Hardback
(228mm x 152mm x 21mm)
Pages: 356
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 10-Aug-2006
Country of Publication: United Kingdom


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Author Biography - Philippe Gille

Philippe Gille is Charge de Recherches, CNRS, Universite de Paris-Sud, Orsay. Tamas Szamuely is Senior Research Fellow, Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest.