{
  "abstract": "Fix a prime $\\ell$. Let $K = \\mathbb{F}_q(t)$ be a global function field such that $\\gcd(q,6) = 1$ and $q \\equiv 1 \\pmod \\ell$. Let $E$ be a non-isotrivial elliptic curve over $K$. Given a fixed monic polynomial $Q$ over $\\mathbb{F}_q$, and assuming some mild conditions on $E$, we show that the rank of $E$ does not change with respect to a positive proportion of $\\mathbb{Z}/\\ell \\mathbb{Z}$ extensions $K(\\sqrt[\\ell]{f})/K$, as $f$ varies over the set of monic polynomials over $\\mathbb{F}_q$ such that $f \\equiv A \\pmod Q$ for any given polynomial $A$. We obtain this result by combining analytic and probabilistic techniques to study the distribution of certain prime Selmer groups of auxiliary abelian varieties constructed from these polynomials $f$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33792",
  "author_total": 2,
  "authors": [
    {
      "name": "Steve Fan"
    },
    {
      "name": "Sun Woo Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx1c8fr079kws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33792",
  "fulltext_url": null,
  "id": "fx1c8fr079kws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33792",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214762722",
  "pdf_url": "https://arxiv.org/pdf/2609.33792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx1c8fr079kws.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rank stability of elliptic curves over $\\mathbb{F}_q(t)$ in residue classes",
  "title_text": "Rank stability of elliptic curves over 𝔽_q(t) in residue classes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/fx1c8fr079kws",
  "venue": "arXiv",
  "versions": []
}