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  • David J. Benson
  • Srikanth Iyengar
  • Henning Krause
Chapter
Part of the Oberwolfach Seminars book series (OWS, volume 43)

Abstract

In this last chapter we put together the various ideas we have been developing in the week’s lectures. The goal, as has been stated often enough, is a classification of the localising subcategories of the stable module category of a finite group, over a field of characteristic p. The strategy of the proof was described in Section 4.1.6, and we begin this chapter at the last step, which is also where the whole story begins, namely, Neeman’s classification of the localising subcategories of the derived category of a commutative noetherian ring. Using a (version of) this result, and a variation of the Bernstein-Gelfand-Gelfand correspondence, we explain how to tackle the case of the homotopy category of complexes of injective modules over an elementary abelian two group. This is the content of Section 5.2. Finally, in the last section, we use Quillen’s results to describe how to pass from arbitrary groups to elementary abelian ones. If the dust settles down, the reader should be able to see a fairly complete proof of our main results for the case p = 2.

Keywords

Prime Ideal Triangulate Category Local Cohomology Homotopy Category Exterior Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • David J. Benson
    • 1
  • Srikanth Iyengar
    • 2
  • Henning Krause
    • 3
  1. 1.Institute of MathematicsUniversity of AberdeenAberdeenUK
  2. 2.Department of MathematicsUniversity of NebraskaLincolnUSA
  3. 3.Fakultät för MathematikUniversität BielefeldBielefeldGermany

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