{
  "abstract": "We extend the Pila-Zannier strategy to Drinfeld modules: we prove analogues of the Manin-Mumford theorem for a product of two Drinfeld modules of equal rank, and of the André-Oort theorem for a product of two Drinfeld modular curves. In characteristic zero, several steps of this strategy rest on $o$-minimality, which has no counterpart over a function field; we replace the counting step by the rigid analytic Pila-Wilkie theorem of Binyamini-Kato, and this appears to be its first arithmetic application. The functional transcendence input, namely an analogue of the Ax-Lindemann theorem in both settings, is established here by an independent point counting argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19952",
  "author_total": 3,
  "authors": [
    {
      "name": "Gal Binyamini"
    },
    {
      "name": "Dmitry Novikov"
    },
    {
      "name": "Francesco Maria Saettone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ty275az3ssj8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19952",
  "fulltext_url": null,
  "id": "8ty275az3ssj8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19952",
  "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": "W7170169501",
  "pdf_url": "https://arxiv.org/pdf/2607.19952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ty275az3ssj8.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2607.19952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves",
  "title_text": "The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/8ty275az3ssj8",
  "venue": "arXiv",
  "versions": []
}