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 \(\Omega ^\bullet _{X/k}\) is equivalent to the unbounded derived category of quasi-coherent right \({\fancyscript{D}}_X\)-modules. We prove that our functors correspond to the functors of the same name for \({\fancyscript{D}}_X\)-modules under Positselski equivalence.