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Let be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study , a monoidal DG category that might be regarded as a categorification of the ring of differential operators on . When is the derived stack of -local systems on a smooth projective curve, we expect to act on both sides of the geometric Langlands correspondence, compatibly with the conjectural Langlands functor. Second, we construct a novel theory of D-modules on derived algebraic stacks. In contrast to usual D-modules, this new theory, to be denoted by , is sensitive to the derived structure. Third, we identify the Drinfeld center of with , the DG category of -modules on the loop stack : = .
Cite this article
Dario Beraldo, The center of the categorified ring of differential operators. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 1999–2049DOI 10.4171/JEMS/1048