Geometric Weil representation in characteristic two

Abstract

AbstractLetkbe an algebraically closed field of characteristic two. LetRbe the ring of Witt vectors of length two overk. We construct a group stack Ĝ overk, the metaplectic extension of the Greenberg realization of$\operatorname{\mathbb{S}p}_{2n}(R)$. We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.