{
  "abstract": "We give a new proof of Faltings' isogeny theorem. More precisely, we show that Yuan's non-archimedean equidistribution theorem can be used to \"pump\" homomorphisms and semisimplicity from finite fields to number fields, thereby reducing Faltings' theorem directly to Tate's theorem. In the appendix joint with Yap, we explain how an ultraproduct variant of our method gives another proof of the Shafarevich conjecture, and hence a new route to the Mordell conjecture via Parshin's trick.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10302",
  "author_total": 2,
  "authors": [
    {
      "name": "Junyi Xie"
    },
    {
      "name": "Ziquan Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ypxrw68pm9vf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10302",
  "fulltext_url": null,
  "id": "3ypxrw68pm9vf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10302",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
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      "arxiv",
      "math.NT"
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    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  ],
  "openalex": "W7212172827",
  "pdf_url": "https://arxiv.org/pdf/2609.10302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ypxrw68pm9vf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.10302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Faltings' Isogeny Theorem via Equidistribution",
  "title_text": "Faltings' Isogeny Theorem via Equidistribution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3ypxrw68pm9vf",
  "venue": "arXiv",
  "versions": []
}