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About this book
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.
The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph.
Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.
Authors and Affiliations
Bibliographic Information
Book Title: Brauer Groups, Hopf Algebras and Galois Theory
Authors: Stefaan Caenepeel
Series Title: K-Monographs in Mathematics
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 1998
Softcover ISBN: 978-1-4020-0346-2Published: 31 March 2002
Series ISSN: 1386-2804
Edition Number: 1
Number of Pages: XVI, 488