Homotopical algebraic context over differential operators. (English) Zbl 1499.14034
Summary: Building on our previous work, we show that the category of non-negatively graded chain complexes of \(\mathcal {D}_X\)-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 B. Toën and G. Vezzosi [Adv. Math. 193, No. 2, 257–372 (2005; Zbl 1120.14012); Homotopical algebraic geometry. II: Geometric stacks and applications. Providence, RI: American Mathematical Society (AMS) (2008; Zbl 1145.14003)].
MSC:
| 14F10 | Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials |
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 14D23 | Stacks and moduli problems |
| 16E35 | Derived categories and associative algebras |
| 18N40 | Homotopical algebra, Quillen model categories, derivators |
| 18M05 | Monoidal categories, symmetric monoidal categories |
Keywords:
derived algebraic geometry; homotopical algebraic context; model category; Batalin-Vilkovisky complex; stack over differential operators; functor of pointsReferences:
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