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

TL;DR

This paper introduces a new stack of G-local systems with restricted variation on the formal punctured disc, embedding it into factorization module categories and developing related functoriality and factorization theories.

Contribution

It defines a novel stack of G-local systems with restricted variation and connects it to factorization modules over Rep(G), advancing the understanding of local systems in algebraic geometry.

Findings

Established properties of the new stack of G-local systems.

Developed a theory of factorization structures in families.

Analyzed functorialities under base curve changes.

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 $\operatorname{Rep}(G)$. Along the way we develop a theory of factorization structures in families and study functorialities of such under changes of the base curve.