Rank varieties and $π$-points for elementary supergroup schemes

We develop a support theory for elementary supergroup schemes, over a field of positive characteristic $p\ge 3$, starting with a definition of a $π$-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and $π$-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra $k[t,τ]/(t^p-τ^2)$, where $t$ has even degree and $τ$ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme.

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