Relative Riemann–Hilbert correspondence in dimension one

Abstract

We prove that, in relative dimension one, the functor RH${}^S$ constructed in a previous work ([9]) as a right quasi-inverse of the solution functor from the bounded derived category of relative $\mathcal{D}$-modules with regular holonomic cohomology to that of complexes with relative constructible cohomology satisfies the left quasi-inverse property in a generic sense.