Quantum parameters of the geometric Langlands theory

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 ${\mathrm{Par}}_G$ of quantum parameters for the geometric Langlands theory. Then we construct a family of (quasi-)twistings parametrized by ${\mathrm{Par}}_G$, whose module categories give rise to twisted $\mathcal{D}$-modules on ${\mathrm{Bun}}_G$ as well as quasi-coherent sheaves on the DG stack ${\mathrm{LocSys}}_G$.

53 pages