Local systems with restricted variation on the formal punctured disc via factorization

Abstract

We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over $\mathrm{Rep}(G)$. Along the way we develop a theory of factorization structures in families and study functorialities of such under changes of the base curve.

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