Model structure on differential graded commutative algebras over the\n ring of differential operators

2015/05/28 by Gennaro Di Brino, di Brino, Gennaro, Damjan Pištalo +3
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1505.07720

openalex publication_date 2015/05/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We construct a cofibrantly generated model structure on the category of\ndifferential non-negatively graded quasi-coherent commutative D_X-algebras,\nwhere D_X is the sheaf of differential operators of a smooth afine algebraic\nvariety X. The paper contains an extensive appendix on D-modules, sheaves\nversus global sections, some more technical model categorical issues, as well\nas on relative Sullivan algebras. This article is the first of a series of\nworks -located at the interface of homotopical algebra, algebraic geometry, and\nmathematical physics - on a derived D-geometric approach to the BV-formalism.\n

Citations

• Model categorical Koszul-Tate resolution for algebras over differential operators

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