{
  "abstract": "Fix a projective unitary Shimura datum satisfying Varshavsky's global Drinfeld uniformization hypotheses at a place $v\\mid p$ of its reflex field $E$. Let $\\mathcal{S}h$ be the base change of the Shimura variety to $\\mathbb C_p$ at a sufficiently small neat finite level. We prove that for every closed reduced algebraic subvariety $Z\\subset\\mathcal{S}h$ with $\\operatorname{dim} Z<\\operatorname{dim} \\mathcal{S}h$, the $p$-adic closure of its full finite adelic Hecke orbit has empty interior in $\\mathcal{S}h(\\mathbb C_p)$. At certain compatible levels, the nowhere density theorem also holds for Shimura varieties associated with a related PEL datum having the same adjoint datum as Varshavsky's. Moreover, for every rational prime $p$ and every integer $d\\geq2$, there is a projective unitary Shimura variety of dimension $d-1$ satisfying these uniformization hypotheses at a place above $p$ for which the nowhere density theorem holds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28869",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8p9y0ze2d72m8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28869",
  "fulltext_url": null,
  "id": "8p9y0ze2d72m8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28869",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223244727",
  "pdf_url": "https://arxiv.org/pdf/2610.28869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8p9y0ze2d72m8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hecke Orbits on Globally Drinfeld-Uniformized Shimura Varieties Are $p$-adically Nowhere Dense",
  "title_text": "Hecke Orbits on Globally Drinfeld-Uniformized Shimura Varieties Are p-adically Nowhere Dense",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/8p9y0ze2d72m8",
  "venue": "arXiv",
  "versions": []
}