Derived Equivalences for Group Rings

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.