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Central Simple Algebras and Galois Cohomology

ISBN-10: 0521861039

ISBN-13: 9780521861038

Edition: 2006

Authors: Philippe Gille, Tam�s Szamuely, B. Bollobas, W. Fulton, A. Katok

List price: $109.99
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Description:

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. It 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

List price: $109.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 8/10/2006
Binding: Hardcover
Pages: 356
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.496
Language: English

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
References
Index