{
  "abstract": "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 $(a,b)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15024",
  "author_total": 1,
  "authors": [
    {
      "name": "Joseph Muller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apqgkm62x0kfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15024",
  "fulltext_url": null,
  "id": "apqgkm62x0kfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15024",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213362824",
  "pdf_url": "https://arxiv.org/pdf/2609.15024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apqgkm62x0kfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.15024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ekedahl-Oort strata meeting the supersingular locus",
  "title_text": "Ekedahl-Oort strata meeting the supersingular locus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/apqgkm62x0kfg",
  "venue": "arXiv",
  "versions": []
}