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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.10313 |
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Table of Contents:
- 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.