15 August 2007 Π-supports for modules for finite group schemes
Eric M. Friedlander, Julia Pevtsova
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Duke Math. J. 139(2): 317-368 (15 August 2007). DOI: 10.1215/S0012-7094-07-13923-1


We introduce the space Π(G) of equivalence classes of π-points of a finite group scheme G and associate a subspace Π(G)M to any G-module M. Our results extend to arbitrary finite group schemes G over arbitrary fields k of positive characteristic and to arbitrarily large G-modules, the basic results about “cohomological support varieties” and their interpretation in terms of representation theory. In particular, we prove that the projectivity of any (possibly infinite-dimensional) G-module can be detected by its restriction along π-points of G. Unlike the cohomological support variety of a G-module M, the invariant MΠ(G)M satisfies good properties for all modules, thereby enabling us to determine the thick, tensor-ideal subcategories of the stable module category of finite-dimensional G-modules. Finally, using the stable module category of G, we provide Π(G) with the structure of a ringed space which we show to be isomorphic to the scheme ProjH(G,k)


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Eric M. Friedlander. Julia Pevtsova. "Π-supports for modules for finite group schemes." Duke Math. J. 139 (2) 317 - 368, 15 August 2007. https://doi.org/10.1215/S0012-7094-07-13923-1


Published: 15 August 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1128.20031
MathSciNet: MR2352134
Digital Object Identifier: 10.1215/S0012-7094-07-13923-1

Primary: 16G10
Secondary: 20C20 , 20G10

Rights: Copyright © 2007 Duke University Press


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Vol.139 • No. 2 • 15 August 2007
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