The Derived Ring of Differential Operators
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 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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