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, Broué'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.
Author(s): Steffen König, Alexander Zimmermann (auth.)
Series: Lecture Notes in Mathematics 1685
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1998
Language: English
Pages: 246
City: Berlin; New York
Tags: Group Theory and Generalizations; K-Theory
Introduction....Pages 1-4
Basic definitions and some examples....Pages 5-32
Rickard's fundamental theorem....Pages 33-50
Some modular and local representation theory....Pages 51-80
Onesided tilting complexes for group rings....Pages 81-104
Tilting with additional structure: twosided tilting complexes....Pages 105-149
Historical remarks....Pages 151-154
On the construction of triangle equivalences....Pages 155-176
Triangulated categories in the modular representation theory of finite groups....Pages 177-198
The derived category of blocks with cyclic defect groups....Pages 199-220
On stable equivalences of Morita type....Pages 221-232
