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Journal of the Institute of Mathematics of Jussieu Journal of the Institute of Mathematics of Jussieu

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RIEMANN–HILBERT CORRESPONDENCE FOR MIXED TWISTOR ${\mathcal{D}}$ -MODULES

Part of: (Co)homology theory Analytic spaces Partial differential equations on manifolds; differential operators Singularities

Published online by Cambridge University Press:  19 May 2017

Teresa Monteiro Fernandes  and
Claude Sabbah
Teresa Monteiro Fernandes
Affiliation:
Centro de Matemática e Aplicações Fundamentais – Centro de investigação Operacional e Departamento de Matemática da FCUL, Edifício C 6, Piso 2, Campo Grande, 1700, Lisboa, Portugal (mtfernandes@fc.ul.pt)
Claude Sabbah
Affiliation:
CMLS, École polytechnique, CNRS, Université Paris-Saclay, F–91128 Palaiseau cedex, France (Claude.Sabbah@polytechnique.edu)http://www.math.polytechnique.fr/perso/sabbah
Corresponding
E-mail address:
mtfernandes@fc.ul.pt
Claude.Sabbah@polytechnique.edu
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Abstract

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.

Keywords

holonomic relative D-module regularity relative constructible sheaf relative perverse sheaf mixed twistor D-module

MSC classification

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32C38: Sheaves of differential operators and their modules, $D$-modules 32S40: Monodromy; relations with differential equations and $D$-modules 32S60: Stratifications; constructible sheaves; intersection cohomology 58J10: Differential complexes ; elliptic complexes
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 3 , May 2019 , pp. 629 - 672
Copyright
© Cambridge University Press 2017 

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Footnotes

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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RIEMANN–HILBERT CORRESPONDENCE FOR MIXED TWISTOR ${\mathcal{D}}$ -MODULES
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