Homotopical algebraic context over differential operators

2017/06/19 by Gennaro Di Brino, Damjan Pištalo, Damjan Pistalo +1 · 2 citations
Mathematics · #Affine transformation #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic closure #Algebraic cycle #Algebraic geometry #Algebraic group #Algebraic number #Algebraic structures and combinatorial models #Algebraic topology #Algebraic variety #Algebraically closed field #Context (archaeology) #Differential (mechanical device) #Differential algebraic geometry #Differential equation #Dimension of an algebraic variety #Field (mathematics) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Number theory #Ordinary differential equation #Physics #Pure mathematics #Variety (cybernetics) #Zero (linguistics) #math.AT

paper · pdf · doi:10.1007/s40062-018-0213-7

arxiv created 2017/06/19 · openalex publication_date 2018/09/18 · arxiv updated 2018/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Building on previous works, we show that the category of non-negatively graded chain complexes of D_X-modules -- where X is a smooth affine algebraic variety over an algebraically closed field of characteristic zero -- fits into a homotopical algebraic context in the sense of Toen and Vezzosi.

Citations

• Homotopy Theories and Model Categories
• D-Modules, Perverse Sheaves, and Representation Theory
• Foundations of Grothendieck Duality for Diagrams of Schemes
• Théorie des Topos et Cohomologie Etale des Schémas
• Model categorical Koszul-Tate resolution for algebras over differential operators
• Model structure on differential graded commutative algebras over the ring of differential operators
• Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes
• Sheaves on Manifolds
• Algebraic Geometry

Cited by

• On Koszul–Tate resolutions and Sullivan models
• Linear Z₂ⁿ-Manifolds and Linear Actions