On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes
Christopher M. Drupieski, Jonathan R. Kujawa

TL;DR
This paper establishes a homeomorphism between the cohomological spectrum of certain infinitesimal supergroup schemes and a variety of supergroup homomorphisms, providing new insights into their support varieties and extending these results to more general cases.
Contribution
It introduces a natural homeomorphism between the cohomological spectrum and a variety of supergroup homomorphisms for infinitesimal elementary supergroup schemes, and extends this to broader classes.
Findings
Homeomorphism between |G| and al N_r(G) for elementary supergroup schemes.
Identification of support varieties for finite-dimensional modules when r=1.
Extension of the homeomorphism to arbitrary infinitesimal unipotent supergroup schemes.
Abstract
We show that if is an infinitesimal elementary supergroup scheme of height , then the cohomological spectrum of is naturally homeomorphic to the variety of supergroup homomorphisms from a certain (non-algebraic) affine supergroup scheme into . In the case , we further identify the cohomological support variety of a finite-dimensional -supermodule as a subset of . 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 to arbitrary infinitesimal unipotent supergroup schemes.
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