{
  "abstract": "Let $\\mathcal D$ be a product of Drinfeld upper half spaces and let $J$ be the corresponding product of projective linear groups acting on $\\mathcal D$. We prove that if $Y$ is a reduced, quasi-compact separated strict $\\mathbb C_p$-analytic space and $f: Y\\to\\mathcal D$ is analytic with $\\dim Y<\\dim\\mathcal D$, then $J f(Y(\\mathbb C_p))$ is closed and nowhere dense in $\\mathcal D(\\mathbb C_p)$. The quasi-compactness assumption is necessary even when the source is a strict rigid analytic curve, while a quasi-compact perfectoid source can still have an orbit closure with nonempty interior. For every finite extension $F/\\mathbb Q_p$ and $d\\geq3$, we construct a closed smooth irreducible non-quasi-compact curve in $Ω_F^{d-1}$ with dense orbit under a fixed diagonal one-parameter subgroup. We also construct a $\\mathbb Q_p$-defined analytic map from the open unit disc to $\\mathbf P^2$ with dense $\\operatorname{PGL}_3(\\mathbb Q_p)$-orbit, and an analytic map from a one-dimensional affinoid perfectoid torus to $\\mathbf P^2$ whose $\\operatorname{PGL}_3(\\mathbb Q_p)$-orbit closure has nonempty interior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12759",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a95rggeaa3x84.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12759",
  "fulltext_url": null,
  "id": "a95rggeaa3x84",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12759",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221559632",
  "pdf_url": "https://arxiv.org/pdf/2610.12759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a95rggeaa3x84.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Rigid Analytic Curve Can Have a Dense $p$-adic Orbit",
  "title_text": "A Rigid Analytic Curve Can Have a Dense p-adic Orbit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/a95rggeaa3x84",
  "venue": "arXiv",
  "versions": []
}