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Representation-theoretic support spaces for finite group schemes
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 2, April 2005
- pp. 379-420
- 10.1353/ajm.2005.0010
- Article
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We introduce the space P(G) of abelian p-points of a finite group scheme over an algebraically closed field of characteristic p > 0. We construct a homeomorphism ΨG: P(G) → Proj |G| from P(G) to the projectivization of the cohomology variety for any finite group G. For an elementary abelian p-group (respectively, an infinitesimal group scheme), P(G) can be identified with the projectivization of the variety of cyclic shifted subgroups (resp., variety of 1-parameter subgroups). For a finite dimensional G-module M, ΨG restricts to a homeomorphism P(G)M → Proj |G|M, thereby giving a representation-theoretic interpretation of the cohomological support variety.