{
  "abstract": "This paper studies a subgroup of the mapping class group of an elliptically fibered $4$-manifold $π: M\\to B$, inspired by number theory. The smooth Mordell-Weil group $\\mathrm{MW}(π)$ is the group of isotopy classes of smooth sections of $π$. We construct a smooth analog of the Shioda-Tate isomorphism, identifying $\\mathrm{MW(π)}$ with the quotient of $H^2(M;\\mathbb{Z})$ by the trivial lattice of $π$. This shows that $\\mathrm{MW}(π)$ can be computed explicitly from $H^2(M;\\mathbb{Z})$. As an application, we show that the natural inclusion of the holomorphic Mordell-Weil group into the smooth one is an isomorphism if and only if $M$ is a rational elliptic surface. As another application, we show that $\\mathrm{MW}(π)$ satisfies a strong version of Nielsen realization: any torsion element of $\\mathrm{MW}(π)$ is represented by a holomorphic translation of $M$ of the same order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05177",
  "author_total": 1,
  "authors": [
    {
      "name": "Maria Morariu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/acwdr2pnbmty1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05177",
  "fulltext_url": null,
  "id": "acwdr2pnbmty1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05177",
  "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.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/acwdr2pnbmty1.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds",
  "title_text": "A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/acwdr2pnbmty1",
  "venue": "arXiv",
  "versions": []
}