{
  "abstract": "Consider a number field $K$, a polarized endomorphism $f:X\\to X$ on a normal projective variety, and a non-exceptional point $α$ for $f$. We show that the extension $K(f^{-\\infty}(α))/K$ generated by the backward orbit of $α$ is virtually abelian if and only if $f$ is an exceptional map with CM and $α$ is $f$-preperiodic. This answers a conjecture of Andrews and Petsche and extends it to higher dimensions. To this end, we develop the theory of exceptional maps on normal projective varieties over $\\mathbb{C}$ and prove that commuting polarized endomorphisms of multiplicatively independent degrees are exceptional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24701",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhuchao Ji"
    },
    {
      "name": "Jiarui Song"
    },
    {
      "name": "Junyi Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drzf53trkx91w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24701",
  "fulltext_url": null,
  "id": "drzf53trkx91w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24701",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.24701",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drzf53trkx91w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24701",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24701"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Exceptional maps and abelian points in backward orbits",
  "title_text": "Exceptional maps and abelian points in backward orbits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/drzf53trkx91w",
  "venue": "arXiv",
  "versions": []
}