{
  "id": "2101.10364",
  "version": "v1",
  "published": "2021-01-25T19:21:13.000Z",
  "updated": "2021-01-25T19:21:13.000Z",
  "title": "Number fields without universal quadratic forms of small rank exist in most degrees",
  "authors": [
    "Vítězslav Kala"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fields that require universal quadratic forms to have arbitrarily large rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-25T19:21:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11R21",
      "11R80"
    ],
    "keywords": [
      "universal quadratic forms",
      "small rank",
      "totally real number fields",
      "arbitrarily large rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}