# Relative regular Riemann-Hilbert correspondence

## TL;DR

This paper establishes a Riemann-Hilbert correspondence for regular holonomic relative D-modules on a product of complex manifolds and curves, linking them to relative perverse and constructible complexes.

## Contribution

It extends the classical Riemann-Hilbert correspondence to a relative setting over a product of complex manifolds and curves, providing a new framework for understanding these objects.

## Key findings

- Proves a correspondence between regular holonomic relative D-modules and relative perverse complexes.
- Establishes a link between relative D-modules and S-constructible complexes.
- Generalizes classical Riemann-Hilbert theory to a relative context.

## Abstract

On the product of a complex manifold $X$ by a complex curve $S$ considered as a parameter space, we show a Riemann-Hilbert correspondence between regular holonomic relative $\mathcal D$-modules (resp. complexes) on the one hand and relative perverse complexes (resp. $S$-$\mathbb{C}$-constructible complexes) on the other hand.