Central Simple Algebras and Galois Cohomology

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. Additional ISBNs 0521861039, 0511223153, 9780521861038, 9780511223150Central Simple Algebras and Galois Cohomology 1st Edition is written by Philippe Gille; Tam�s Szamuely and published by Cambridge University Press. ISBNs for Central Simple Algebras and Galois Cohomology are 9780511223150, 0511223153 and the print ISBNs are 9780521861038, 0521861039. Additional ISBNs include 0521861039, 0511223153, 9780521861038, 9780511223150.