发表机构
National Center for Theoretic Sciences, National Taiwan University（台湾大学理论科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文给出了特征p>2时主极化阿贝尔簇模栈中EO层与超奇异轨迹相交的显式组合判据，并证明了渐近几乎所有p-秩为零的EO层均相交，同时应用于酉PEL Shimura簇给出下界。
AI 中文摘要
我们给出了在特征 $p > 2$ 的 $g$ 维主极化阿贝尔簇的模栈中，一个Ekedahl-Oort（EO）层与超奇异轨迹相交的显式组合判据。该判据通过将基本仿射Deligne-Lusztig簇的非空性判据转化为关于索引EO层的初等序列的显式条件而获得。此外，我们给出了与超奇异轨迹不相交的 $p$-秩为零的EO层数量的显式界。由此，我们证明了渐近地几乎所有的 $p$-秩为零的EO层都与超奇异轨迹相交。作为应用，我们还给出了在签名 $(a,b)$ 的酉PEL Shimura簇上与超奇异轨迹相交的EO层数量的一个下界。
英文摘要
We give an explicit combinatorial criterion for an Ekedahl-Oort (EO) stratum in the moduli stack of principally polarized abelian varieties of dimension $g$ in characteristic $p > 2$ to meet the supersingular locus. The criterion is obtained by translating a non-emptiness criterion for basic affine Deligne-Lusztig varieties, into an explicit condition on the elementary sequences indexing the EO strata. Furthermore, we give explicit bounds for the number of EO strata of $p$-rank zero which are disjoint from the supersingular locus. As a result, we prove that asymptotically almost every EO stratum of $p$-rank zero meets the supersingular locus. As an application, we also give a lower bound for the number of EO strata meeting the supersingular locus on unitary PEL Shimura varieties of signature $(a,b)$.
Comments25 pages, this version is updated with a reference to recent work of Shimada (arXiv:2609.27198)
