\'Etale metaplectic covers of reductive group schemes

TL;DR

This paper provides a linear algebraic framework for understanding reduced étale 4-cocycles on the classifying stack of a reductive group scheme, enabling the definition of the Langlands dual of a metaplectic cover.

Contribution

It introduces a linear algebraic description of étale 4-cocycles and interprets them as parameters for metaplectic covers, also defining their Langlands dual.

Findings

Linear algebraic description of étale 4-cocycles

Interpretation of cocycles as parameters of metaplectic covers

Definition of the Langlands dual of a metaplectic cover

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.