LEADER 03129nam 2200637 450 001 996466864103316 005 20220905195942.0 010 $a3-540-69748-9 024 7 $a10.1007/BFb0096366 035 $a(CKB)1000000000437328 035 $a(SSID)ssj0000322520 035 $a(PQKBManifestationID)12117606 035 $a(PQKBTitleCode)TC0000322520 035 $a(PQKBWorkID)10283687 035 $a(PQKB)10389205 035 $a(DE-He213)978-3-540-69748-0 035 $a(MiAaPQ)EBC5595163 035 $a(Au-PeEL)EBL5595163 035 $a(OCoLC)1076255483 035 $a(MiAaPQ)EBC6841949 035 $a(Au-PeEL)EBL6841949 035 $a(OCoLC)1292355060 035 $a(PPN)155181386 035 $a(EXLCZ)991000000000437328 100 $a20220905d1998 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDerived equivalences for group rings /$fSteffen Ko?nig, Alexander Zimmermann with contributions by Bernhard Keller 205 $a1st ed. 1998. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[1998] 210 4$d©1998 215 $a1 online resource (X, 246 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1685 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-64311-7 320 $aIncludes bibliographical references (pages [233]-243) and index. 327 $aBasic 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. 330 $aA self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1685. 606 $aGroup rings 606 $aAlgebra, Homological 615 0$aGroup rings. 615 0$aAlgebra, Homological. 676 $a512.2 700 $aKo?nig$b Steffen$f1961-$061856 702 $aZimmermann$b Alexander$f1964- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466864103316 996 $aDerived equivalences for group rings$9261850 997 $aUNISA