{
  "abstract": "We prove an analog of the Ax-Schanuel theorem for the Drinfeld $j$-function in odd characteristic. Roughly speaking, if the graph of $\\boldsymbol{j}\\colonΩ^n\\rightarrow\\mathbb{A}^n_{\\mathbb{C}_\\infty}$ and its derivatives has an atypical intersection $\\mathcal{V}$ with an algebraic variety, then $\\mathcal{V}$ projects to a weakly-special subvariety in $\\mathbb{A}^n_{\\mathbb{C}_\\infty}$. More generally, we prove a positive characteristic analog of the differential Galois theoretic Ax-Schanuel theorem of Blázquez-Sanz, Casale, Freitag and Nagloo. Our main theorem for $\\boldsymbol{j}$ follows by applying this result to a suitable foliation. A theorem of Pink allows us to conclude that the special varieties in the sense of Blázquez-Sanz et al. in this context agree with the classical weakly-special subvarieties in the Drinfeld sense.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37595",
  "author_total": 3,
  "authors": [
    {
      "name": "Gal Binyamini"
    },
    {
      "name": "Dmitry Novikov"
    },
    {
      "name": "Francesco Maria Saettone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbvsnmnj6pndr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37595",
  "fulltext_url": null,
  "id": "bbvsnmnj6pndr",
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  "landing_url": "https://arxiv.org/abs/2609.37595",
  "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": "W7214987241",
  "pdf_url": "https://arxiv.org/pdf/2609.37595",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbvsnmnj6pndr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37595",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37595"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ax-Schanuel for the Drinfeld $j$-function",
  "title_text": "Ax-Schanuel for the Drinfeld j-function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/bbvsnmnj6pndr",
  "venue": "arXiv",
  "versions": []
}