Modules over the de Rham cohomology spectrum

2016/11/30 by Dmitri Pavlov, Pavlov, Dmitri, Jakob Scholbach +1
Mathematics · #14F10 #14F40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1611.10134

openalex publication_date 2016/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_* D_X, f^* := D_X f^! D_Y (f: X → 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.

Citations

• The six operations in equivariant motivic homotopy theory

Related

• Holonomic \mathscrD-modules on rigid analytic varieties
• DG-modules over de Rham DG-algebra
• Relative strongly regular holonomic D-modules and the Riemann-Hilbert correspondence
• t-Structures for Relative \D-Modules and t-Exactness of\n the de Rham Functor
• Motivic structures in non-commutative geometry