Some cases of Oort's conjecture about Newton polygons
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909310034903040 |
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| author | Pries, Rachel |
| author_facet | Pries, Rachel |
| contents | This paper contains a method to prove the existence of smooth curves in positive characteristic whose Jacobians have unusual Newton polygon. Using this method, I give a new proof that there exist supersingular curves of genus $4$ for every prime $p$. More generally, for every prime $p$ and every $g \geq 4$, I prove that every Newton polygon whose $p$-rank is at least $g-4$ occurs for a smooth curve of genus $g$. In addition, I resolve some cases of Oort's conjecture about Newton polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some cases of Oort's conjecture about Newton polygons Pries, Rachel Number Theory Algebraic Geometry 20: primary 11G10, 11G20, 11M38, 14H10, 14H40, secondary 14G10, 14G15 This paper contains a method to prove the existence of smooth curves in positive characteristic whose Jacobians have unusual Newton polygon. Using this method, I give a new proof that there exist supersingular curves of genus $4$ for every prime $p$. More generally, for every prime $p$ and every $g \geq 4$, I prove that every Newton polygon whose $p$-rank is at least $g-4$ occurs for a smooth curve of genus $g$. In addition, I resolve some cases of Oort's conjecture about Newton polygons. |
| title | Some cases of Oort's conjecture about Newton polygons |
| topic | Number Theory Algebraic Geometry 20: primary 11G10, 11G20, 11M38, 14H10, 14H40, secondary 14G10, 14G15 |
| url | https://arxiv.org/abs/2306.11080 |