We show that if G is an infinitesimal elementary supergroup scheme of height ≤ r, then the cohomological spectrum |G| of G is naturally homeomorphic to the variety N_r(G) of supergroup homomorphisms ρ: M_r → G from a certain (non-algebraic) affine supergroup scheme 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 N_1(G). We then discuss how our methods, when combined with recently-announced results by

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... , Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism N_r(G) |G| to arbitrary infinitesimal unipotent supergroup schemes.