---

＜電子ブック＞
Representations of Finite Groups: Local Cohomology and Support / by David J. Benson, Srikanth Iyengar, Henning Krause
(Oberwolfach Seminars. ISSN:22965041 ; 43)

版	1st ed. 2012.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2012
大きさ	X, 105 p : online resource
著者標目	*Benson, David J author Iyengar, Srikanth author Krause, Henning author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Commutative algebra LCSH:Commutative rings LCSH:Associative rings LCSH:Associative algebras FREE:Group Theory and Generalizations FREE:Commutative Rings and Algebras FREE:Associative Rings and Algebras
一般注記	Preface -- 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 The 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-0260-4

 類似資料