(t\)-Structures for Relative \(\mathcal{D}\)-Modules and \(t\)-Exactness of the de Rham Functor

This paper is a contribution to the study of relative holonomic \(\mathcal{D}\)-modules. Contrary to the absolute case, the standard \(t\)-structure on holonomic \(\mathcal{D}\)-modules is not preserved by duality and hence the solution functor is no longer \(t\)-exact with respect to the canonical,...

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Bibliographic Details
Published in:arXiv.org 2018-06
Main Authors: Fiorot, Luisa, Teresa Monteiro Fernandes
Format: Article
Language:English
Subjects:
Modules
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Summary:This paper is a contribution to the study of relative holonomic \(\mathcal{D}\)-modules. Contrary to the absolute case, the standard \(t\)-structure on holonomic \(\mathcal{D}\)-modules is not preserved by duality and hence the solution functor is no longer \(t\)-exact with respect to the canonical, resp. middle-perverse, \(t\)-structures. We provide an explicit description of these dual \(t\)-structures. When the parameter space is 1-dimensional, we use this description to prove that the solution functor as well as the relative Riemann-Hilbert functor are \(t\)-exact with respect to the dual \(t\)-structure and to the middle-perverse one while the de Rham functor is \(t\)-exact for the canonical, resp. middle-perverse, \(t\)-structures and their duals.
ISSN:2331-8422