ENGLISH

Central Simple Algebras and Galois Cohomology

By Tamás Szamuely , Philippe Gille

Book information

Publisher
Cambridge University Press
Year
2006
ISBN
0521861039, 9780521861038, 9780511226359
Open Library ID
OL22734524M
Language
english
Format
PDF
Filesize
5 MB (4943178 bytes)
Series
Cambridge Studies in Advanced Mathematics 00
Pages
356\355
Topic
Mathematics Algebra
Scanned
yes
Time added
2011-04-11 19:55:47

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.

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