t-Structures for relative D-modules and t-exactness of the de Rham functor

This paper is a contribution to the study of relative holonomic D-modules. Contrary to the absolute case, the standard t-structure on holonomic 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-structure....

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Bibliographic Details
Published in:Journal of algebra 2018-09, Vol.509, p.419-444
Main Authors: Fiorot, Luisa, Monteiro Fernandes, Teresa
Format: Article
Language:English
Subjects:
De Rham functor
Relative [formula omitted]-modules
t-structure
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Summary:This paper is a contribution to the study of relative holonomic D-modules. Contrary to the absolute case, the standard t-structure on holonomic 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-structure. We provide an explicit description of these dual t-structures. 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-structure and their duals.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2018.05.011