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arXiv · 2303.16083

The Derived Ring of Differential Operators

Andy Jiang
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Abstract

By reading a standard formula for the ring of Grothendieck differential operators in a derived way, we construct a derived (sheaf of) ring of Grothendieck differential operators for Noetherian schemes $X$ separated and finite-type over a base $S$, when the map $X \to S$ is finite tor-amplitude. Using this ring of differential operators, we (re-)develop the theory of $D$-modules from scratch and show an equivalence of categories between $D$-modules using our definition and crystals over the infinitesimal site.

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Andy Jiang. 2023-03-28. The Derived Ring of Differential Operators. https://arxiv.org/abs/2303.16083

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