{
  "abstract": "The shape of a number field $K$ of degree $n\\geq2$ is the similarity class of the lattice obtained by projecting $\\mathscr{O}_K$ orthogonally away from the rational line in Minkowski space. It defines a point in the space of shapes of rank-$(n-1)$ lattices, $\\mathscr{S}_{n-1}:=\\mathrm{GL}_{n-1}(\\mathbb{Z})\\backslash \\mathrm{GL}_{n-1}(\\mathbb{R})/\\mathrm{GO}_{n-1}(\\mathbb{R})$, where $\\mathrm{GO}_{n-1}(\\mathbb{R})$ is the group of orthogonal similitudes. Let $G$ be a fixed nontrivial finite abelian group, and let $K/\\mathbb{Q}$ vary over tamely ramified Galois extensions with Galois group isomorphic to $G$. We study the variation of the shapes of such number fields in $\\mathscr S_{n-1}$, where $n=|G|$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19311",
  "author_total": 1,
  "authors": [
    {
      "name": "Anwesh Ray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ykh36hg2ybgs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19311",
  "fulltext_url": null,
  "id": "1ykh36hg2ybgs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19311",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7222172924",
  "pdf_url": "https://arxiv.org/pdf/2610.19311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ykh36hg2ybgs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Shapes of tame abelian number fields",
  "title_text": "Shapes of tame abelian number fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/1ykh36hg2ybgs",
  "venue": "arXiv",
  "versions": []
}