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arXiv · 2409.14322

Duality of differential operators and algebraic de Rham cohomology

Caleb Ji·Casimir Kothari·Oliver Li·Svetlana Makarova·Shubhankar Sahai·Sridhar Venkatesh
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Abstract

Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies to two-term complexes of this type. We apply this to give a new proof of Poincar\'e duality for relative algebraic de Rham cohomology.

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Caleb Ji, Casimir Kothari, Oliver Li, Svetlana Makarova, Shubhankar Sahai, Sridhar Venkatesh. 2024-09-22. Duality of differential operators and algebraic de Rham cohomology. https://arxiv.org/abs/2409.14322

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