Coherent sheaves, sheared D-modules, and Hochschild cochains

Dario Beraldo; Kevin Lin; Wyatt Reeves

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arXiv · 2410.10692

Coherent sheaves, sheared D-modules, and Hochschild cochains

Dario Beraldo·Kevin Lin·Wyatt Reeves

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Abstract

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.

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BibTeX RIS

Dario Beraldo, Kevin Lin, Wyatt Reeves. 2024-10-14. Coherent sheaves, sheared D-modules, and Hochschild cochains. https://arxiv.org/abs/2410.10692

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