Vanishing and a counterexample for Witt divisorial sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909821700145152 |
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| author | Lemcke, Niklas |
| author_facet | Lemcke, Niklas |
| contents | First we refine the duality theory for Witt divisorial sheaves on smooth projective varieties over a perfect field of positive characteristic. Building on previous work [Lem22], we remove the residual derived limit to obtain a cleaner isomorphism. As an application, we prove a Ramanujam-type vanishing theorem for Witt divisorial sheaves of nef and big divisors on surfaces. Finally, we show that a surface constructed by Langer [Lan16] with a divisor constructed by Cascini and Tanaka [CT18] gives a counterexample to Kawamata-Viehweg-type vanishing of Witt divisorial sheaves in dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_17893 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vanishing and a counterexample for Witt divisorial sheaves Lemcke, Niklas Algebraic Geometry 14F30, 14F17, 14J26 First we refine the duality theory for Witt divisorial sheaves on smooth projective varieties over a perfect field of positive characteristic. Building on previous work [Lem22], we remove the residual derived limit to obtain a cleaner isomorphism. As an application, we prove a Ramanujam-type vanishing theorem for Witt divisorial sheaves of nef and big divisors on surfaces. Finally, we show that a surface constructed by Langer [Lan16] with a divisor constructed by Cascini and Tanaka [CT18] gives a counterexample to Kawamata-Viehweg-type vanishing of Witt divisorial sheaves in dimension two. |
| title | Vanishing and a counterexample for Witt divisorial sheaves |
| topic | Algebraic Geometry 14F30, 14F17, 14J26 |
| url | https://arxiv.org/abs/2305.17893 |