Eric Friedlander,  Northwestern
Julia Pevtsova,  IAS

Representation-theoretic support spaces for finite group schemes.
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 $\\Psi_G: P(G) \\to
Proj(|G|)$ 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 $M$, $\\Psi_G$
restricts to a homeomorphism $P(G)_M \\to Proj(|G|_M)$, thereby
giving a representation-theoretic interpretation of the
cohomological support variety.