Central Simple Algebras and Galois Cohomology
Aug 2006 · Cambridge Studies in Advanced Mathematics Book 101 · Cambridge University Press
Ebook
26
Pages
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About this ebook
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.
About the author
Philippe Gille is Chargé de Recherches, CNRS, Université de Paris-Sud, Orsay.
Tamás Szamuely is Senior Research Fellow, Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest.
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