Coherent sheaves, sheared D-modules, and Hochschild cochains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929552197943296 |
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| author | Beraldo, Dario Lin, Kevin Reeves, Wyatt |
| author_facet | Beraldo, Dario Lin, Kevin Reeves, Wyatt |
| contents | We show that the category of ind-coherent sheaves on a quasi-smooth scheme is naturally tensored over the category of sheared D-modules on its shifted cotangent bundle, commuting with its natural action of categorified Hoschschild cochains. We prove that it defines a Morita equivalence as such. We then extend these results to quasi-smooth Artin stacks.
As a consequence of our formalism, we are able to articulate a precise sense in which the space of unramified automorphic functions over a function field localizes over the stack of arithmetic Arthur parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coherent sheaves, sheared D-modules, and Hochschild cochains Beraldo, Dario Lin, Kevin Reeves, Wyatt Algebraic Geometry We show that the category of ind-coherent sheaves on a quasi-smooth scheme is naturally tensored over the category of sheared D-modules on its shifted cotangent bundle, commuting with its natural action of categorified Hoschschild cochains. We prove that it defines a Morita equivalence as such. We then extend these results to quasi-smooth Artin stacks. As a consequence of our formalism, we are able to articulate a precise sense in which the space of unramified automorphic functions over a function field localizes over the stack of arithmetic Arthur parameters. |
| title | Coherent sheaves, sheared D-modules, and Hochschild cochains |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.10692 |