The Derived Ring of Differential Operators

2023/03/28 by Andy Jiang, Jiang, Andy
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2303.16083

openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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