Relative strongly regular holonomic $\mathcal{D}$-modules and the Riemann-Hilbert correspondence

Abstract

We introduce the notion of strong regular holonomic ${\mathcal{D}}_{X\times S/S}$-module and we prove that the functor ${\mathrm{RH}}^S$ introduced by T. Monteiro Fernandes and C. Sabbah in [14] takes image in ${\mathsf{D}}_{\mathrm{srhol}}^{\mathrm{b}}({\mathcal{D}}_{X\times S/S})$ (complexes of ${\mathcal{D}}_{X\times S/S}$-module whose cohomologies are strongly regular). We prove that for $\dim X=\dim S=1$ the functor solution functor ${}^{\mathrm{p}}\mathrm{Sol}$ restricted to ${\mathsf{D}}_{\mathrm{srhol}}^{\mathrm{b}}({\mathcal{D}}_{X\times S/S})$ is an equivalence of categories with quasi-inverse ${\mathrm{RH}}^S$.

13 pages

References in corpus (1)

• Riemann-Hilbert correspondence for mixed twistor D-Modules