For any étale metaplectic cover of a reductive p-adic group, a cover of each extended pure inner form is constructed, and the paper shows the set of forms whose Weissman obstruction vanishes is a torsor under a Galois coinvariant group.
\'Etale metaplectic covers of reductive group schemes
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abstract
Given a reductive group scheme $G$, we give a linear algebraic description of reduced \'etale $4$-cocycles on its classifying stack $\mathrm B(G)$. These cocycles form a $2$-groupoid, which we interpret as parameters of metaplectic covers of $G$. We use our linear algebraic description to define the Langlands dual of a metaplectic cover.
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What are the extended pure inner forms of a cover?
For any étale metaplectic cover of a reductive p-adic group, a cover of each extended pure inner form is constructed, and the paper shows the set of forms whose Weissman obstruction vanishes is a torsor under a Galois coinvariant group.