{
  "abstract": "We extend the method of Van Woerden \\cite{woerden} to totally real and CM number fields to obtain an upper bound for the number of $\\GLo-$equivalence classes of perfect forms. Moreover, by considering appropriate barycentric subdivisions of the Voronoi tessellation, we extend these estimates to the number of $\\GLo$-orbits of $k$-dimensional faces of the Voronoi tessellation. As a consequence, we improve the asymptotic order of the bounds for the torsion part of $K_m(\\rint)$ obtained by Soulé \\cite{soule_hermitian_bounds} and Houriet \\cite{Juliet_PHD}. We emphasise the improvement of the general bound for $F=\\mathbb Q$, unchanged since Soulé's work, and the independence of the discriminant exponent from the field degree for totally real and CM fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06300",
  "author_total": 1,
  "authors": [
    {
      "name": "Alejandro de la Torre Durán"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dsn080pvrbbpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06300",
  "fulltext_url": null,
  "id": "dsn080pvrbbpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06300",
  "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.GT"
    ],
    [
      "arxiv",
      "math.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06300",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dsn080pvrbbpr.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06300",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06300"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Perfect Forms and Torsion Bounds in Algebraic $K$-Theory over Totally Real and CM Fields",
  "title_text": "Perfect Forms and Torsion Bounds in Algebraic K-Theory over Totally Real and CM Fields",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/dsn080pvrbbpr",
  "venue": "arXiv",
  "versions": []
}