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 | | Brauer Groups, Hopf Algebras and Galois Theory (K-Monographs in Mathematics) by Stefaan Caenepeel ISBN-10: 9780792348290 ISBN-10: 0-7923-4829-X ISBN-13: 9780792348290 ISBN-13: 978-0-7923-4829-0 Hardcover 1998-01-31 Springer Find Lowest Price |
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Product Description 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 etale 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. | ||