{
  "abstract": "We prove that every de Rham $p$-adic local system on a smooth projective curve over a $p$-adic field is potentially semistable; that is, it becomes semistable after pulling back along a finite cover of the curve. This establishes a relative version of the classical $p$-adic monodromy theorem of Berger and André--Kedlaya--Mebkhout. Along the way, we show that every $p$-adic differential equation near a type I\\!V point on a curve becomes trivial after a finite étale extension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11106",
  "author_total": 3,
  "authors": [
    {
      "name": "Hansheng Diao"
    },
    {
      "name": "Yong Suk Moon"
    },
    {
      "name": "Zijian Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zvgabt53wh7j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11106",
  "fulltext_url": null,
  "id": "9zvgabt53wh7j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11106",
  "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": "W7212306947",
  "pdf_url": "https://arxiv.org/pdf/2609.11106",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zvgabt53wh7j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2609.11106",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A $p$-adic monodromy theorem for curves",
  "title_text": "A p-adic monodromy theorem for curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/9zvgabt53wh7j",
  "venue": "arXiv",
  "versions": []
}