Étale metaplectic covers of reductive group schemes

Abstract

Given a reductive group scheme $\mathrm{G}$, we give a linear-algebraic description of reduced étale $4$-cocycles on its classifying stack $\mathrm{B}(\mathrm{G})$. These cocycles form a $2$-groupoid, which we interpret as parameters of metaplectic covers of $\mathrm{G}$. We use our linear-algebraic description to define the Langlands dual of a metaplectic cover.