03131nam 2200637 450 991014630060332120220905195942.03-540-69748-910.1007/BFb0096366(CKB)1000000000437328(SSID)ssj0000322520(PQKBManifestationID)12117606(PQKBTitleCode)TC0000322520(PQKBWorkID)10283687(PQKB)10389205(DE-He213)978-3-540-69748-0(MiAaPQ)EBC5595163(Au-PeEL)EBL5595163(OCoLC)1076255483(MiAaPQ)EBC6841949(Au-PeEL)EBL6841949(OCoLC)1292355060(PPN)155181386(EXLCZ)99100000000043732820220905d1998 uy 0engurnn|008mamaatxtccrDerived equivalences for group rings /Steffen König, Alexander Zimmermann with contributions by Bernhard Keller1st ed. 1998.Berlin, Germany ;New York, New York :Springer,[1998]©19981 online resource (X, 246 p.) Lecture Notes in Mathematics,0075-8434 ;1685Bibliographic Level Mode of Issuance: Monograph3-540-64311-7 Includes bibliographical references (pages [233]-243) and index.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, 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.Lecture notes in mathematics (Springer-Verlag) ;1685.Group ringsAlgebra, HomologicalGroup rings.Algebra, Homological.512.2König Steffen1961-61856Zimmermann Alexander1964-MiAaPQMiAaPQMiAaPQBOOK9910146300603321Derived equivalences for group rings261850UNINA