Details

Autor(en) / Beteiligte

• K©œnig, Steffen
• Zimmermann, Alexander

Titel

Derived Equivalences for Group Rings

Ist Teil von

• Lecture Notes in Mathematics : 1685

Ort / Verlag

Berlin, Heidelberg : Springer Berlin Heidelberg

Erscheinungsjahr

1998

Link zum Volltext

• Volltext

Beschreibungen/Notizen

• Basic definitions and some examples -- Rickard's fundamental theorem -- Some modular and local representation theory -- Onesided tilting complexes for group rings -- Tilting with additional structure: twosided tilting complexes -- Historical remarks -- On the construction of triangle equivalences -- Triangulated categories in the modular representation theory of finite groups -- The derived category of blocks with cyclic defect groups -- On stable equivalences of Morita type
• 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