Supersingular Ekedahl-Oort strata and Oort's conjecture
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917322952802304 |
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| author | Karemaker, Valentijn Yu, Chia-Fu |
| author_facet | Karemaker, Valentijn Yu, Chia-Fu |
| contents | Let $\mathcal{A}_g$ be the moduli space over $\overline{\mathbb{F}}_p$ of $g$-dimensional principally polarised abelian varieties, where $p$ is a prime. We show that if $g$ is even and $p\geq 5$, then every geometric generic member in the maximal supersingular Ekedahl-Oort stratum in $\mathcal{A}_g$ has automorphism group $\{ \pm 1\}$. This confirms Oort's conjecture in the case of $p\geq 5$ and even $g$. We also separately prove Oort's conjecture for $g=4$ and any prime $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supersingular Ekedahl-Oort strata and Oort's conjecture Karemaker, Valentijn Yu, Chia-Fu Number Theory Algebraic Geometry 14K10 (14K15, 11G10, 51A50) Let $\mathcal{A}_g$ be the moduli space over $\overline{\mathbb{F}}_p$ of $g$-dimensional principally polarised abelian varieties, where $p$ is a prime. We show that if $g$ is even and $p\geq 5$, then every geometric generic member in the maximal supersingular Ekedahl-Oort stratum in $\mathcal{A}_g$ has automorphism group $\{ \pm 1\}$. This confirms Oort's conjecture in the case of $p\geq 5$ and even $g$. We also separately prove Oort's conjecture for $g=4$ and any prime $p$. |
| title | Supersingular Ekedahl-Oort strata and Oort's conjecture |
| topic | Number Theory Algebraic Geometry 14K10 (14K15, 11G10, 51A50) |
| url | https://arxiv.org/abs/2406.19748 |