Duke Mathematical Journal
- Duke Math. J.
- Volume 139, Number 2 (2007), 317-368.
-supports for modules for finite group schemes
We introduce the space of equivalence classes of -points of a finite group scheme and associate a subspace to any -module . Our results extend to arbitrary finite group schemes over arbitrary fields of positive characteristic and to arbitrarily large -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) -module can be detected by its restriction along -points of . Unlike the cohomological support variety of a -module , the invariant satisfies good properties for all modules, thereby enabling us to determine the thick, tensor-ideal subcategories of the stable module category of finite-dimensional -modules. Finally, using the stable module category of , we provide with the structure of a ringed space which we show to be isomorphic to the scheme
Duke Math. J., Volume 139, Number 2 (2007), 317-368.
First available in Project Euclid: 31 July 2007
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Friedlander, Eric M.; Pevtsova, Julia. $\Pi$ -supports for modules for finite group schemes. Duke Math. J. 139 (2007), no. 2, 317--368. doi:10.1215/S0012-7094-07-13923-1. https://projecteuclid.org/euclid.dmj/1185891825