{
  "abstract": "Let $p$ be a prime number. In 1986, David Lampert asked if one expands a $\\mathbf{Q}_p$-algebraic number as a $p$-adic Hahn series, then what is the possible order type of its support? In 2001, Kedlaya made a vague conjecture that the possible ordinals can only be finite ordinals, $ω$ and $ω^ω$, where $ω$ is the first infinite ordinal. In this article, we solve Lampert's problem by confirming Kedlaya's intuition. Moreover, we completely characterize the $\\mathbf{Q}_p$-algebraic numbers with order type of support at most $ω$. As an application, we determine the bi-algebraic set of the $p$-adic shadow map.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13014",
  "author_total": 2,
  "authors": [
    {
      "name": "Shanwen Wang"
    },
    {
      "name": "Yijun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ba6m0282ew7r6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13014",
  "fulltext_url": null,
  "id": "ba6m0282ew7r6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13014",
  "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": "W7221551296",
  "pdf_url": "https://arxiv.org/pdf/2610.13014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba6m0282ew7r6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The order types of the supports of $p$-adic algebraic Hahn series",
  "title_text": "The order types of the supports of p-adic algebraic Hahn series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ba6m0282ew7r6",
  "venue": "arXiv",
  "versions": []
}