Liftability and vanishing theorems for Fano threefolds in positive characteristic I
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929758147706880 |
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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 for the case when $|-K_X|$ is very ample and the Picard group is generated by $ω_X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Liftability and vanishing theorems for Fano threefolds in positive characteristic I Kawakami, Tatsuro Tanaka, Hiromu Algebraic Geometry 14J45, 13A35, 14F17 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 for the case when $|-K_X|$ is very ample and the Picard group is generated by $ω_X$. |
| title | Liftability and vanishing theorems for Fano threefolds in positive characteristic I |
| topic | Algebraic Geometry 14J45, 13A35, 14F17 |
| url | https://arxiv.org/abs/2503.10236 |