Modules over the de Rham cohomology spectrum

Abstract

We show that the bounded derived category of regular holonomic D-modules on a smooth variety is equivalent to the homotopy catgory of compact (or constructible) modules over the motivic ring spectrum $H_{dR}$ representing algebraic de Rham cohomology. This equivalence is compatible with the six functors on both sides. This way, the classical functors in the world of D-modules, $f_{!}:=D_Y{f}_{\ast }{D}_X,f^{\ast }:=D_X{f}^{!}{D}_Y$ ($f:X\to Y$), are conceptually explained and embedded into a larger and more flexible framework. We also apply this equivalence to obtain a motivic t-structure on $H_{dR}$-modules on not necessarily smooth schemes.

arXiv commentThe paper is temporarily withdrawn because of an error in the proof of Theorem 3.3.2

References in corpus (8)

• Higher Topos Theory
• Algebras and modules in monoidal model categories
• Triangulated categories of mixed motives
• Equivalences of monoidal model categories
• The six operations in equivariant motivic homotopy theory
• Mixed Weil cohomologies
• The Beilinson regulator is a map of ring spectra
• Rectification of Deligne's mixed Hodge structures