{"paper":{"title":"Relative strongly regular holonomic ${\\mathcal{D}}$-modules and the Riemann-Hilbert correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luisa Fiorot, Teresa Monteiro Fernandes","submitted_at":"2018-11-17T12:16:55Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07151","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}