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Central simple algebras and Galois cohomology /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Central simple algebras and Galois cohomology // Philippe Gille, Tamás Szamuely.
其他題名:	Central Simple Algebras & Galois Cohomology
作者:	Gille, Philippe,
其他作者:	Szamuely, Tamás,
面頁冊數:	1 online resource (ix, 343 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Galois cohomology. -
電子資源:	https://doi.org/10.1017/CBO9780511607219
ISBN:	9780511607219 (ebook)

Central simple algebras and Galois cohomology /
Gille, Philippe,1968-

Central simple algebras and Galois cohomology /Central Simple Algebras & Galois CohomologyPhilippe Gille, Tamás Szamuely. - 1 online resource (ix, 343 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;101. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Quaternion algebras -- Central simple algebras and Galois descent -- Techniques from group cohomology -- The cohomological Brauer group -- Severi-Brauer varieties -- Residue maps -- Milnor K-theory -- The Merkurjev-Suslin theorem -- Symbols in positive characteristic -- A breviary of algebraic geometry.

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.

ISBN: 9780511607219 (ebook)Subjects--Topical Terms:

1444742
Galois cohomology.

LC Class. No.: QA612.3 / .G55 2006

Dewey Class. No.: 514.23

Central simple algebras and Galois cohomology /
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505 0 $a Quaternion algebras -- Central simple algebras and Galois descent -- Techniques from group cohomology -- The cohomological Brauer group -- Severi-Brauer varieties -- Residue maps -- Milnor K-theory -- The Merkurjev-Suslin theorem -- Symbols in positive characteristic -- A breviary of algebraic geometry.
520 $a 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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700 1 $a Szamuely, Tamás, $e author. $3 1444741
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