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Brauer Groups, Hopf Algebras and Galois Theory

Brauer Groups, Hopf Algebras and Galois Theory

Paperback

Series: K-Monographs in Mathematics, Book 4

AlgebraGeometry

ISBN10: 1402003463
ISBN13: 9781402003462
Publisher: Springer
Published: Mar 31 2002
Pages: 488
Weight: 1.54
Height: 1.07 Width: 6.22 Depth: 9.36
Language: English

This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included.

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Caenepeel, Stefaan

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Algebra