Pure injectives and the spectrum of the cohomology ring of a finite group

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Abstract

For a finite group G and a field k of prime characteristic, we study certain pure injective kG-modules in terms of the spectrum of the group cohomology ring H* (G, k). For instance, we construct a map from the projective variety Proj (H* (G, k)) to the Ziegler spectrum of indecomposable pure injective kG-modules. We identify the module corresponding to a generic point for a component of the variety; it is generic in the sense of Crawley-Boevey and closely related to a certain Rickard idempotent module. We include also a complete classification of all kG-modules which arise as a direct summand of a (possibly infinite) product of syzygies of the trivial module k.

Original languageEnglish
Pages (from-to)23-51
Number of pages28
JournalJournal für die reine und angewandte Mathematik
Volume542
DOIs
Publication statusPublished - 2002

Keywords

  • INFINITELY GENERATED MODULES
  • PHANTOM MAPS
  • CATEGORY
  • COMPLEXITY
  • VARIETIES

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