Quantum parameters of the geometric Langlands theory

TL;DR

This paper introduces a new algebraic stack of quantum parameters for the geometric Langlands program and constructs a family of twistings that connect twisted D-modules and quasi-coherent sheaves on moduli stacks.

Contribution

It defines the algebraic stack of quantum parameters and constructs a family of twistings linking different categories in the geometric Langlands framework.

Findings

Established the algebraic stack of quantum parameters for G.

Constructed a family of twistings parametrized by this stack.

Connected twisted D-modules on Bun_G with quasi-coherent sheaves on LocSys_G.

Abstract

Fix a smooth, complete algebraic curve $X$ over an algebraically closed field $k$ of characteristic zero. To a reductive group $G$ over $k$, we associate an algebraic stack $\operatorname{Par}_G$ of quantum parameters for the geometric Langlands theory. Then we construct a family of (quasi-)twistings parametrized by $\operatorname{Par}_G$, whose module categories give rise to twisted $\mathcal D$-modules on $\operatorname{Bun}_G$ as well as quasi-coherent sheaves on the DG stack $\operatorname{LocSys}_G$.