Naive co-contra correspondence for $\mathcal D$-modules

Abstract

We construct a triangulated equivalence between the derived categories of quasi-coherent and contraherent $\mathcal A$-modules for a quasi-coherent quasi-algebra $\mathcal A$ over a quasi-compact semi-separated scheme $X$. The sheaf of rings of differential operators $\mathcal D$ (or fiberwise differential operators for a smooth morphism of schemes) is the thematic example of a quasi-coherent quasi-algebra.

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