000 04008nam a22004935i 4500
001 978-3-0348-0260-4
003 DE-He213
005 20140220083253.0
007 cr nn 008mamaa
008 111114s2012 sz | s |||| 0|eng d
020 _a9783034802604
_9978-3-0348-0260-4
024 7 _a10.1007/978-3-0348-0260-4
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.2
_223
100 1 _aBenson, David J.
_eauthor.
245 1 0 _aRepresentations of Finite Groups: Local Cohomology and Support
_h[electronic resource] /
_cby David J. Benson, Srikanth Iyengar, Henning Krause.
264 1 _aBasel :
_bSpringer Basel,
_c2012.
300 _aX, 105p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOberwolfach Seminars ;
_v43
505 0 _aPreface -- 1 Monday -- 1.1 Overview -- 1.2 Modules over group algebras -- 1.3 Triangulated categories -- 1.4 Exercises -- 2 Tuesday -- 2.1 Perfect complexes over commutative rings -- 2.2 Brown representability and localization -- 2.3 The stable module category of a finite group -- 2.4 Exercises -- 3 Wednesday -- 3.1 -- 3.2 Koszul objects and support -- 3.3 The homotopy category of injectives -- 3.4 Exercises -- 4 Thursday -- 4.1 Stratifying triangulated categories -- 4.2 Consequences of stratification -- 4.3 The Klein four group -- 4.4 Exercises -- 5 Friday -- 5.1 Localising subcategories of D(A) -- 5.2 Elementary abelian 2-groups -- 5.3 Stratification for arbitrary finite groups -- 5.4 Exercises -- A Support for modules over commutative rings -- Bibliography -- Index.
520 _aThe seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGroup theory.
650 1 4 _aMathematics.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aCommutative Rings and Algebras.
650 2 4 _aAssociative Rings and Algebras.
700 1 _aIyengar, Srikanth.
_eauthor.
700 1 _aKrause, Henning.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034802598
830 0 _aOberwolfach Seminars ;
_v43
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0260-4
912 _aZDB-2-SMA
999 _c101723
_d101723