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Representations of Finite Groups: Local Cohomology and Support

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. T...

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Bibliographic Details
Main Authors: Benson, David J., Iyengar, Srikanth (Author), Krause, Henning (Author)
Format: eBook
Language:English
Published: Basel Springer Basel 2012, 2012
Edition:1st ed. 2012
Series:Oberwolfach Seminars
Subjects:
Associative Rings And Algebras
Commutative Algebra
Group Theory
Rings (algebra)
Commutative Rings And Algebras
Commutative Rings
Associative Rings
Group Theory And Generalizations
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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

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