{
  "abstract": "Let $K$ be a $p$-adic field. We study the arithmetic theory of abeloid varieties over $K$. Our aims are twofold. First, we study the theory of rigid analytic 1-motives, which will be viewed as a tool to describe degeneration of abeloid varieties, similarly as in the classical algebraic setting. Our key new results are the equivalence between formal (resp. log formal) 1-motives over $\\mathcal{O}_K$ and rigid analytic 1-motives with good (resp. semi-stable) reduction over $K$, and the Néron-Ogg-Shafarevich criterion for the good (resp. semi-stable) reduction of rigid analytic 1-motives. In particular, we construct log formal 1-motives and log $p$-divisible groups over $\\mathcal{O}_K$ from semi-stable abeloid varieties over $K$. Next, we study the conjugate uniformization of an arbitrary abeloid variety $A$ over $K$. This is a type of $p$-adic uniformization initiated by Iovita--Morrow--Zaharescu in case of abelian varieties with good reduction. Our approach here is based on Fargues' theory of $p$-divisible rigid analytic groups. In fact, we view the theory of conjugate uniformization as a study of rational points of dualizable $p$-divisible rigid analytic groups in terms of their classification Hodge--Tate triples. Along the way, we construct $p$-divisible rigid analytic groups from rigid analytic 1-motives.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25424",
  "author_total": 3,
  "authors": [
    {
      "name": "Khai-Hoan Nguyen-Dang"
    },
    {
      "name": "Xu Shen"
    },
    {
      "name": "Heer Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fq12ph92pz6h0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25424",
  "fulltext_url": null,
  "id": "fq12ph92pz6h0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25424",
  "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": "W7204438144",
  "pdf_url": "https://arxiv.org/pdf/2608.25424",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fq12ph92pz6h0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.25424",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25424"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rigid analytic 1-motives and conjugate uniformization of abeloid varieties",
  "title_text": "Rigid analytic 1-motives and conjugate uniformization of abeloid varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/fq12ph92pz6h0",
  "venue": "arXiv",
  "versions": []
}