{
  "abstract": "We provide a general construction of infinite Hopf-Galois extensions from a direct system of finite Hopf-Galois extensions. We then apply this framework to extensions generated by division points on elliptic curves. Specifically, for a number field $K$ and an elliptic curve $E/K$ of rank at least $1$ with $P\\in E(K)$ of infinite order, we consider for each integer $n\\geq 2$ the extension $L_n=K(Q_n)$, where $Q_n\\in E(\\overline{K})$ is such that $nQ_n=P$. We show that the finite-level extensions $L_n/K$ need not be Hopf-Galois, and we give sufficient conditions for them to be so. We then prove that the infinite extension $L_\\infty=\\bigcup_{n\\geq 2}L_n$ of $K$ is potentially Hopf-Galois, meaning it becomes Hopf-Galois after a finite extension of the base field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06253",
  "author_total": 1,
  "authors": [
    {
      "name": "Leolin Nkuete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x47hx5efy55r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06253",
  "fulltext_url": null,
  "id": "5x47hx5efy55r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06253",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06253",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x47hx5efy55r.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06253",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06253"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hopf-Galois Structures on Extensions Arising from Division Points on Elliptic Curves",
  "title_text": "Hopf-Galois Structures on Extensions Arising from Division Points on Elliptic Curves",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/5x47hx5efy55r",
  "venue": "arXiv",
  "versions": []
}