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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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| _version_ | 1866913993991389184 |
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| author | Fiorot, Luisa Fernandes, Teresa Monteiro |
| author_facet | Fiorot, Luisa Fernandes, Teresa Monteiro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10313 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On relative constructible sheaves and integral transforms Fiorot, Luisa Fernandes, Teresa Monteiro Algebraic Geometry 32S60, 18F30, 14C35 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. |
| title | On relative constructible sheaves and integral transforms |
| topic | Algebraic Geometry 32S60, 18F30, 14C35 |
| url | https://arxiv.org/abs/2310.10313 |