Lecture Notes in Mathematics

By: Steffen KÃ¶nig, B. Keller (Contribution by), M. Linckelmann (Contribution by)

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Paperback | 20 May 1998

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260 Pages

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A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Brou©'s conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.

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Non-Fiction Mathematics Algebra Mathematical Foundation Set Theory Groups & Group Theory Geometry Algebraic Geometry Topology Algebraic Topology

Introduction	p. 1
Basic definitions and some examples	p. 5
Rickard's fundamental theorem	p. 33
Some modular and local representation theory	p. 51
Onesided tilting complexes for group rings	p. 81
Tilting with additional structure: twosided tilting complexes	p. 105
Historical remarks	p. 151
On the construction of triangle equivalences	p. 155
Triangulated Categories in the Modular Representation Theory of Finite Groups	p. 177
The derived category of blocks with cyclic defect groups	p. 199
On stable equivalences of Morita type	p. 221
Bibliography	p. 233
Index	p. 244
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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