On relative constructible sheaves and integral transforms

The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible sheaves and for relative regular holonomic \(\mathcal D\)-modules...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Fiorot, Luisa, Teresa Monteiro Fernandes
Format: Article
Language:English
Subjects:
Homology
Isomorphism
Online Access:Get full text
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Summary:The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible sheaves and for relative regular holonomic \(\mathcal D\)-modules and prove they induce relative equivalences of categories. The third is to introduce and study the notions of relative constructible functions and relative Euler-Poincaré index. We prove that the relative Euler-Poincaré index provides an isomorphism between the Grothendieck group of the derived category of complexes with bounded relative \(\mathbb R\)-constructible cohomology and the ring of relative constructible functions.
ISSN:2331-8422