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  1. Home
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  3. Central Simple Algebras and Galois Cohomology
  • Cited by 211
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
2006
Online ISBN:
9780511607219
DOI:
https://doi.org/10.1017/CBO9780511607219
Subjects:
Mathematics (general), Mathematics, Geometry and Topology, Algebra
Series:
Cambridge Studies in Advanced Mathematics (101)
Information

Book 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. The book is suitable as a textbook for graduate students and as a reference for researchers working in algebra, algebraic geometry or K-theory.

Reviews

'The presentation of material is reader-friendly, arguments are clear and concise, exercises at the end of every chapter are original and stimulating, the appendix containing some basic notions from algebra and algebraic geometry is helpful. To sum up, the book under review can be strongly recommended to everyone interested in the topic.'

Source: Zentralblatt MATH

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