Overview

This volume is devoted to the Brauer group of a commutative ring and related invariants. Part one presents a 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 two 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 one 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 three. 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.

Full Product Details

Author:   Stefaan Caenepeel
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1998 ed.
Volume:   4
Dimensions:   Width: 15.60cm , Height: 2.50cm , Length: 23.40cm
Weight:   0.771kg
ISBN:  

9781402003462

ISBN 10:   1402003463
Pages:   488
Publication Date:   31 March 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I The Brauer group of a commutative ring.- 1 Morita theory for algebras without a unit.- 2 Azumaya algebras and Taylor-Azumaya algebras.- 3 The Brauer group.- 4 Central separable algebras.- 5 Amitsur cohomology and étale cohomology.- 6 Cohomological interpretation of the Brauer group.- II Hopf algebras and Galois theory.- 7 Hopf algebras.- 8 Galois objects.- 9 Cohomology over Hopf algebras.- 10 The group of Galois (co)objects.- 11 Some examples.- III The Brauer-Long group of a commutative ring.- 12 H-Azumaya algebras.- 13 The Brauer-Long group of a commutative ring.- 14 The Brauer group of Yetter-Drinfel’d module algebras.- A Abelian categories and homological algebra.- A.1 Abelian categories.- A.2 Derived functors.- B Faithfully flat descent.- C Elementary algebraic K-theory.

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