Relative strongly regular holonomic D-modules and the Riemann-Hilbert correspondence

2018/11/17 by Luisa Fiorot, Fiorot, Luisa, Térésa Monteiro Fernandes +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1811.07151

openalex publication_date 2018/11/17 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of strong regular holonomic D_X× S/S-module and we prove that the functor RH^S introduced by T. Monteiro Fernandes and C. Sabbah in [14] takes image in D^b_srhol(D_X× S/S) (complexes of D_X× S/S-module whose cohomologies are strongly regular). We prove that for dim X=dim S=1 the functor solution functor ^pSol restricted to D^b_srhol(D_X× S/S) is an equivalence of categories with quasi-inverse RH^S.

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