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arXiv · 2406.19748

Supersingular Ekedahl-Oort strata and Oort's conjecture

Valentijn Karemaker·Chia-Fu Yu
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Abstract

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 $p$.

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Valentijn Karemaker, Chia-Fu Yu. 2024-06-28. Supersingular Ekedahl-Oort strata and Oort's conjecture. https://arxiv.org/abs/2406.19748

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