2005/10/13 by Carlos Simpson, Carlos T. Simpson, Simpson, Carlos T.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.math/0510269
openalex publication_date 2005/10/13 · arxiv created 2008/04/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a locally geometric ∞-stack MHod(X,Perf) of perfect complexes with λ-connection structure on a smooth projective variety X. This maps to A 1 / Gm, so it can be considered as the Hodge filtration of its fiber over 1 which is MDR(X,Perf), parametrizing complexes of DX-modules which are OX-perfect. We apply the result of Toen-Vaquie that Perf(X) is locally geometric. The proof of geometricity of the map MHod(X,Perf) → Perf(X) uses a Hochschild-like notion of weak complexes of modules over a sheaf of rings of differential operators. We prove a strictification result for these weak complexes, and also a strictification result for complexes of sheaves of O-modules over the big crystalline site.