{
  "abstract": "Given a field $L$ and polynomial $f(x)/L$, one can consider the indices of the profinite iterated monodromy groups formed over the ground field within the profinite iterated monodromy groups over elements transcendental over $L$. For any countable Hilbertian field $k$, we show random Galois fixed field extensions almost surely make the indices infinite over all ground field elements, with certain conditions on $f(x)$. This is a generalization of a result in arXiv:2012.03076 by Dittmann and Kadets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40017",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Gotshall"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c93qbngdrdd44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40017",
  "fulltext_url": null,
  "id": "c93qbngdrdd44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40017",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c93qbngdrdd44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infinite Index",
  "title_text": "Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infinite Index",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/c93qbngdrdd44",
  "venue": "arXiv",
  "versions": []
}