  We show that if $G$ is an infinitesimal elementary supergroup scheme of
height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally
homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms
$\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine
supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further
identify the cohomological support variety of a finite-dimensional
$G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our
methods, when combined with recently-announced results by Benson, Iyengar,
Krause, and Pevtsova, can be applied to extend the homeomorphism
$\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup
schemes.
