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arXiv · 1611.10134

Modules over the de Rham cohomology spectrum

Dmitri Pavlov·Jakob Scholbach
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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, $f_! := D_Y f_* D_X, f^* := D_X f^! D_Y$ ($f: X \to Y$), 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.

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Dmitri Pavlov, Jakob Scholbach. 2016-11-30. Modules over the de Rham cohomology spectrum. https://arxiv.org/abs/1611.10134

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