DG-modules over de Rham DG-algebra

Abstract

For a morphism of smooth schemes over a regular affine base we define functors of derived direct image and extraordinary inverse image on coderived categories of DG-modules over de Rham DG-algebras. Positselski proved that for a smooth algebraic variety $X$ over a field $k$ of characteristic zero the coderived category of DG-modules over ${\Omega }_{X/k}^{\bullet }$ is equivalent to the unbounded derived category of quasi-coherent right ${\mathcal{D}}_X$-modules. We prove that our functors correspond to the functors of the same name for ${\mathcal{D}}_X$-modules under Positselski equivalence.

arXiv comment21 pages