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

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 \({\mathsf{D}}^{\mathrm{b}}_{\mathrm{srhol}}({\mathcal{D}}_{{X\times S}/S})\) (compl...

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Bibliographic Details
Published in:arXiv.org 2018-11
Main Authors: Fiorot, Luisa, Teresa Monteiro Fernandes
Format: Article
Language:English
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Modules
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Summary: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 \({\mathsf{D}}^{\mathrm{b}}_{\mathrm{srhol}}({\mathcal{D}}_{{X\times S}/S})\) (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 \({\mathsf{D}}^{\mathrm{b}}_{\mathrm{srhol}}({\mathcal{D}}_{{X\times S}/S})\) is an equivalence of categories with quasi-inverse \({\mathrm{RH}}^S\).
ISSN:2331-8422