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, Broue'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.