# The de Rham functor for logarithmic D-modules

## TL;DR

This paper extends the theory of logarithmic D-modules by developing a six-functor framework, defining a logarithmic de Rham functor, and relating it to duality and classical filtrations, thereby enriching the geometric understanding of these modules.

## Contribution

It introduces a logarithmic de Rham functor for D-modules, connecting it to duality and classical filtrations, and deepens the six-functor theory for logarithmic D-modules.

## Key findings

- The de Rham functor maps logarithmic D-modules to graded sheaves with finitely generated stalks.
- The functor intertwines D-module duality with Poincaré-Verdier duality on the Kato-Nakayama space.
- The grading relates to the Kashiwara-Malgrange V-filtration for holonomic D-modules.

## Abstract

In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato-Nakayama space. For holonomic modules we show that the associated sheaves have finitely generated stalks and that the de Rham functor intertwines duality for D-modules with a version of Poincar\'e-Verdier duality on the Kato-Nakayama space. Finally, we explain how the grading on the Kato-Nakayama space is related to the classical Kashiwara-Malgrange V-filtration for holonomic D-modules.