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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.15665 |
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| _version_ | 1866917021743054848 |
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| author | Buccisano, Carlo |
| author_facet | Buccisano, Carlo |
| contents | The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given by Beraldo, Nuiten and Toën-Vezzosi, on a (nice) derived scheme yield equivalent symmetric monoidal $\infty$-categories. We deduce this as a corollary of more general statements about Chevalley-Eilenberg cohomology of dg-Lie algebroids, proving a conjecture by E. Pavia, and about the relation between representations of a dg-Lie algebroid and some class of ind-coherent sheaves on the associated formal moduli problem, which can be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On derived D-modules and their several definitions Buccisano, Carlo Algebraic Geometry Algebraic Topology The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given by Beraldo, Nuiten and Toën-Vezzosi, on a (nice) derived scheme yield equivalent symmetric monoidal $\infty$-categories. We deduce this as a corollary of more general statements about Chevalley-Eilenberg cohomology of dg-Lie algebroids, proving a conjecture by E. Pavia, and about the relation between representations of a dg-Lie algebroid and some class of ind-coherent sheaves on the associated formal moduli problem, which can be of independent interest. |
| title | On derived D-modules and their several definitions |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2510.15665 |