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  • Teresa Monteiro Fernandes (a1) and Claude Sabbah (a2)


We introduce the notion of regularity for a relative holonomic ${\mathcal{D}}$ -module in the sense of Monteiro Fernandes and Sabbah [Internat. Math. Res. Not. (21) (2013), 4961–4984]. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of relative constructible complexes is essentially surjective by constructing a right quasi-inverse functor. When restricted to relative ${\mathcal{D}}$ -modules underlying a regular mixed twistor ${\mathcal{D}}$ -module, this functor satisfies the left quasi-inverse property.



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The research of TMF was supported by Fundação para a Ciência e Tecnologia UID/MAT/04561/2013. The research of CS was supported by the grant ANR-13-IS01-0001-01 of the Agence nationale de la recherche.



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