Beraldo, D;
(2021)
Tempered D-modules and Borel–Moore homology vanishing.
Inventiones Mathematicae
10.1007/s00222-021-01036-2.
(In press).
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Abstract
We characterize the tempered part of the automorphic Langlands category D(BunG) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Σ a smooth affine curve, the Borel–Moore homology of the indscheme Maps(Σ,G) vanishes.
| Type: | Article |
|---|---|
| Title: | Tempered D-modules and Borel–Moore homology vanishing |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00222-021-01036-2 |
| Publisher version: | https://doi.org/10.1007/s00222-021-01036-2 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| 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/10124413 |
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