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