  We develop a support theory for elementary supergroup schemes, over a field
of positive characteristic $p\ge 3$, starting with a definition of a
$\pi$-point generalising cyclic shifted subgroups of Carlson for elementary
abelian groups and $\pi$-points of Friedlander and Pevtsova for finite group
schemes. These are defined in terms of maps from the graded algebra
$k[t,\tau]/(t^p-\tau^2)$, where $t$ has even degree and $\tau$ 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.
