{
  "abstract": "We prove Steinness over $\\breve{\\mathbf{Q}}_p$ for the basic local Shimura tower attached to $G=\\mathrm{GL}_n$, $μ=(1,1,0^{n-2})$, with basic Newton slope $2/n$, for every odd $n\\ge3$, at every finite level and for every prime $p$. The proof proceeds by constructing global analytic functions from the crystalline period map, proving compactness of their sublevel sets via a perfectoid normalization of Tate lattices, and showing that the resulting function map to affine space is finite. The key geometric inputs are the Fargues--Fontaine realization of the universal cover, a normalized determinant on the rank-two locus, and an integral PEL realization over $W(\\overline{\\mathbf{F}}_p)$ used to produce bounded global Hodge generators. The integral constructions include the prime $p=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22921",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiawei Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d546xhms052pz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22921",
  "fulltext_url": null,
  "id": "d546xhms052pz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22921",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213998910",
  "pdf_url": "https://arxiv.org/pdf/2609.22921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d546xhms052pz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Steinness of the Basic $\\mathrm{GL}_n$ Local Shimura Tower in Odd Rank",
  "title_text": "Steinness of the Basic GL_n Local Shimura Tower in Odd Rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/d546xhms052pz",
  "venue": "arXiv",
  "versions": []
}