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Central Simple Algebras and Galois Cohomology (Paperback, 2nd Revised edition)
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Central Simple Algebras and Galois Cohomology (Paperback, 2nd Revised edition)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 19 working days
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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.
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