Steffen König, Alexander Zimmermann

Derived Equivalences for Group Rings (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 246
• Erscheinungstermin: 14. November 2006
• Englisch
• ISBN-13: 9783540697480
• Artikelnr.: 53151526

Inhaltsangabe

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.