{
  "abstract": "Let $k_0$ be a field of characteristic $0$, and let $C/k_0$ be a smooth geometrically integral curve of positive genus with $C(k_0)=\\varnothing$. We prove that the regular inverse Galois problem is solvable over every field existentially closed in the class of $k_0$-fields avoiding $C$, including the curve-excluding fields of Johnson and the author. To this end, we show that for every finite group $G$, there is a parameter variety over $\\mathbb Q$ whose function field admits a regular realization of $G$ without adding points to $C$. Finally, we establish $\\mathrm{RIGP}$ over the variety-excluding fields of Szachniewicz and the author, when the excluded variety is a locally closed subvariety of an abelian variety.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19689",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinhe Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9qhwg213nnzq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19689",
  "fulltext_url": null,
  "id": "a9qhwg213nnzq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19689",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222162191",
  "pdf_url": "https://arxiv.org/pdf/2610.19689",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9qhwg213nnzq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19689",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19689"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The regular inverse Galois problem over fields avoiding a curve",
  "title_text": "The regular inverse Galois problem over fields avoiding a curve",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/a9qhwg213nnzq",
  "venue": "arXiv",
  "versions": []
}