Liftability and vanishing theorems for Fano threefolds in positive characteristic II
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913827522609152 |
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| author | Kawakami, Tatsuro Tanaka, Hiromu |
| author_facet | Kawakami, Tatsuro Tanaka, Hiromu |
| contents | In our series of papers, we prove that smooth Fano threefolds in positive characteristic lift to the ring of Witt vectors. Moreover, we show that they satisfy Akizuki-Nakano vanishing, $E_1$-degeneration of the Hodge to de Rham spectral sequence, and torsion-freeness of Crystalline cohomologies. In this paper, we establish these results except when $|-K_X|$ is very ample and the Picard group is generated by $ω_X$. To this end, we show that an arbitrary smooth Fano threefold is quasi-$F$-split when the Picard number or the Fano index is larger than one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liftability and vanishing theorems for Fano threefolds in positive characteristic II Kawakami, Tatsuro Tanaka, Hiromu Algebraic Geometry In our series of papers, we prove that smooth Fano threefolds in positive characteristic lift to the ring of Witt vectors. Moreover, we show that they satisfy Akizuki-Nakano vanishing, $E_1$-degeneration of the Hodge to de Rham spectral sequence, and torsion-freeness of Crystalline cohomologies. In this paper, we establish these results except when $|-K_X|$ is very ample and the Picard group is generated by $ω_X$. To this end, we show that an arbitrary smooth Fano threefold is quasi-$F$-split when the Picard number or the Fano index is larger than one. |
| title | Liftability and vanishing theorems for Fano threefolds in positive characteristic II |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.04764 |