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 cha...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: König, Steffen (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Zimmermann, Alexander (http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
Έκδοση:1st ed. 1998.
Σειρά:Lecture Notes in Mathematics, 1685
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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245 1 0 |a Derived Equivalences for Group Rings  |h [electronic resource] /  |c by Steffen König, Alexander Zimmermann. 
250 |a 1st ed. 1998. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 1998. 
300 |a X, 246 p.  |b online resource. 
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490 1 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1685 
505 0 |a 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. 
520 |a 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. 
650 0 |a Group theory. 
650 0 |a K-theory. 
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830 0 |a Lecture Notes in Mathematics,  |x 0075-8434 ;  |v 1685 
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