Countability of relative Fourier-Mukai partners
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916444497772544 |
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| author | Kurama, Riku |
| author_facet | Kurama, Riku |
| contents | Anel and Toën proved that a smooth projective complex variety has only countably many smooth projective Fourier-Mukai partners up to isomorphism. This is generalized in the Stacks Project to the case where the varieties are smooth proper over an arbitrary algebraically closed field. This note will upgrade the proof of the latter reference to show that a smooth proper scheme over a noetherian base has only countably many relative Fourier-Mukai partners up to isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Countability of relative Fourier-Mukai partners Kurama, Riku Algebraic Geometry Anel and Toën proved that a smooth projective complex variety has only countably many smooth projective Fourier-Mukai partners up to isomorphism. This is generalized in the Stacks Project to the case where the varieties are smooth proper over an arbitrary algebraically closed field. This note will upgrade the proof of the latter reference to show that a smooth proper scheme over a noetherian base has only countably many relative Fourier-Mukai partners up to isomorphism. |
| title | Countability of relative Fourier-Mukai partners |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.14064 |