Beraldo, D;
(2021)
Deligne-Lusztig duality on the stack of local systems.
Journal fur die Reine und Angewandte Mathematik
10.1515/crelle-2021-0030.
(In press).
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Abstract
In the setting of the geometric Langlands conjecture, we argue that the phenomenon of divergence at infinity on BunG (that is, the difference between !-extensions and * -extensions) is controlled, Langlands-dually, by the locus of semisimple ˇG-local systems. To see this, we first rephrase the question in terms of Deligne–Lusztig duality and then study the Deligne–Lusztig functor DLspecGacting on the spectral Langlands DG category IndCohN(LSG). We prove that DLspecG is the projection IndCohN (LSG)↠QCoh (LSG), followed by the action of a coherent D-module StG∈D(LSG), which we call the SteinbergD-module. We argue that StG might be regarded as the dualizing sheaf of the locus of semisimple G-local systems. We also show that DL spec G, while far from being conservative, is fully faithful on the subcategory of compact objects.
| Type: | Article |
|---|---|
| Title: | Deligne-Lusztig duality on the stack of local systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/crelle-2021-0030 |
| Publisher version: | https://doi.org/10.1515/crelle-2021-0030 |
| Language: | English |
| Additional information: | © 2021 Dario Beraldo, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. |
| 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.ucl.ac.uk/id/eprint/10131752 |
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