{
  "abstract": "We construct infinitely many Galois extensions $M/\\mathbb{Q}$ with dihedral group of order ten, quadratic subfield $\\mathbb{Q}(i)$, and Bloch lattice index $Q_2(M)=5$. More precisely, we specify a Chebotarev set of rational primes of density $1/50$. For every prime $\\ell$ in this set, at least two of four mixed cyclic quintic extensions of $\\mathbb{Q}(i)$ of conductor $(25\\ell)$ have this index and satisfy $K_2(O_M)(5)\\simeq(\\mathbb{Z}/5)^2$. A two-dimensional cup-product pencil selects the extensions. Generalized Bockstein maps, integral co-descent, and a motivic genus formula then determine the tame kernel and the subfield Bloch-lattice index. The result is unconditional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24043",
  "author_total": 1,
  "authors": [
    {
      "name": "Zheng Huimin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2647drtmgqp0f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24043",
  "fulltext_url": null,
  "id": "2647drtmgqp0f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24043",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223011414",
  "pdf_url": "https://arxiv.org/pdf/2610.24043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2647drtmgqp0f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Dihedral fields with Bloch lattice index five and quadratic subfield Q(i)",
  "title_text": "Dihedral fields with Bloch lattice index five and quadratic subfield Q(i)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2647drtmgqp0f",
  "venue": "arXiv",
  "versions": []
}