rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Representations of Finite Groups: Local Cohomology and Support
  name:
    name part: Benson, David J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Iyengar, Srikanth.
    role:
      role term: author.
  name:
    name part: Krause, Henning.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 105 p. online resource.
  abstract: 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.
  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.
  note: by David J. Benson, Srikanth Iyengar, Henning Krause.
  subject:
    topic: Mathematics
  subject:
    topic: Associative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: Group theory
  subject:
    topic: Mathematics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: Associative Rings and Algebras
  classification: QA174-183
  classification: 512.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Oberwolfach Seminars ; 43
  identifier: 9783034802604
  identifier: http://dx.doi.org/10.1007/978-3-0348-0260-4
  record info:
    record creation date: 111114
    record change date: 20151204183738.0
    record identifier: 978-3-0348-0260-4