On Frobenius liftability of surface singularities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909105056120832 |
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| author | Kawakami, Tatsuro Takamatsu, Teppei |
| author_facet | Kawakami, Tatsuro Takamatsu, Teppei |
| contents | We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for $F$-pure surface pairs and Bogomolov-Sommese vanishing for globally $F$-split surface pairs. These results were previously known to hold in characteristic $p>5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Frobenius liftability of surface singularities Kawakami, Tatsuro Takamatsu, Teppei Algebraic Geometry 13A35, 14F10, 14B05 We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for $F$-pure surface pairs and Bogomolov-Sommese vanishing for globally $F$-split surface pairs. These results were previously known to hold in characteristic $p>5$. |
| title | On Frobenius liftability of surface singularities |
| topic | Algebraic Geometry 13A35, 14F10, 14B05 |
| url | https://arxiv.org/abs/2402.08152 |