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 $\operatorname{ LocSys}_G$.
Categories: math.AG