{
  "abstract": "We establish a function field analogue of a recent conjecture of Andrews--Petsche. Our main result characterizes abelian dynamical Galois groups to be precisely the isotrivial ones, whenever the degree of the polynomial is smaller than $p$, the characteristic of the field. The proof of this characterization is achieved in four independent steps as follows: $$\\text{Abelian} \\implies \\text{Finite ramification} \\implies \\text{PCF map} \\implies \\text{Isotrivial map} \\implies \\text{Isotrivial pair}, $$ and works more generally for maps with a superattracting fixed point. We observe that this chain of implications is sharp in the degree: as soon as one reaches $p$ there are new non-isotrivial examples coming from Drinfeld modules. We propose a full conjectural classification in all degrees, taking into account all of the new exotic examples coming from Drinfeld modules and their associated Lattès maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24920",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Ferraguti"
    },
    {
      "name": "Patrick Ingram"
    },
    {
      "name": "Carlo Pagano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8asvfsbs1zfth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24920",
  "fulltext_url": null,
  "id": "8asvfsbs1zfth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24920",
  "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/2609.24920",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8asvfsbs1zfth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24920",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24920"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Abelian dynamical Galois groups over global function fields",
  "title_text": "Abelian dynamical Galois groups over global function fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/8asvfsbs1zfth",
  "venue": "arXiv",
  "versions": []
}