Relative Regular Riemann-Hilbert correspondence II

TL;DR

This paper extends the theory of relative regular holonomic D-modules to higher-dimensional parameter spaces, establishing a general relative Riemann-Hilbert correspondence beyond the one-dimensional case.

Contribution

It generalizes the relative Riemann-Hilbert correspondence to arbitrary-dimensional parameter spaces for regular holonomic D-modules.

Findings

Established the theory of relative regular holonomic D-modules for complex manifolds of any dimension.

Proved the main functorial properties of these modules.

Extended the relative Riemann-Hilbert correspondence to higher-dimensional parameter spaces.

Abstract

We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting the relative Riemann-Hilbert correspondence proved in a previous work in the one-dimensional case.