{
  "abstract": "For a finite extension of global fields $K/k$, the norm map $N_{K/k} : K^\\times \\to k^\\times$ extends to a map on idèle groups. The Hasse norm principle holds if every element of $k^\\times$ that is a norm everywhere locally is also a norm globally. In this paper, we study the statistics of the Hasse norm principle in a setting that is out of reach in the number field context, namely that of $A_4$-quartic extensions. We show that failures of the Hasse norm principle are generally rare for $A_4$-quartic extensions of global function fields $\\mathbb{F}_q(t)$. We achieve this by introducing a decorated Hurwitz space parametrising the failures of the Hasse norm principle and then using the Chebotarev density theorem to estimate their frequency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02444",
  "author_total": 4,
  "authors": [
    {
      "name": "Anand Deopurkar"
    },
    {
      "name": "Rachel Newton"
    },
    {
      "name": "Vaidehee Thatte"
    },
    {
      "name": "Rosa Winter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qsq6fvtz74gb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02444",
  "fulltext_url": null,
  "id": "5qsq6fvtz74gb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02444",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7207849283",
  "pdf_url": "https://arxiv.org/pdf/2609.02444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qsq6fvtz74gb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Hasse norm principle for $A_4$-quartic extensions of global function fields",
  "title_text": "The Hasse norm principle for A_4-quartic extensions of global function fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/5qsq6fvtz74gb",
  "venue": "arXiv",
  "versions": []
}