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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2510.15665 |
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- 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.