Abstract

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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 379-420
Launched on MUSE
2005-03-28
Open Access
No
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