Beraldo, D;
(2021)
The center of the categorified ring of differential operators.
Journal of the European Mathematical Society
, 23
(6)
pp. 1999-2049.
10.4171/JEMS/1048.
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Abstract
Let Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study H(Y), a monoidal DG category that might be regarded as a categorification of the ring of differential operators on Y. When Y=LSG is the derived stack of G-local systems on a smooth projective curve, we expect H(LSg) 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 Dder, is sensitive to the derived structure. Third, we identify the Drinfeld center of H(Y) with Dder(LY), the DG category of Dder-modules on the loop stack LY: = Y×Y×YY.
| Type: | Article |
|---|---|
| Title: | The center of the categorified ring of differential operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/JEMS/1048 |
| Publisher version: | https://doi.org/10.4171/JEMS/1048 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Derived algebraic geometry, coherent sheaves, formal completions, Hochschild cohomology, DG categories, Drinfeld center, D-modules |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10122877 |
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