{
  "id": "2407.20781",
  "version": "v1",
  "published": "2024-07-30T12:34:14.000Z",
  "updated": "2024-07-30T12:34:14.000Z",
  "title": "Universality lifting from a general base field",
  "authors": [
    "Vitezslav Kala",
    "Daejun Kim",
    "Seok Hyeong Lee"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given a totally real number field $F$, we show that there are only finitely many totally real extensions of $K$ of a fixed degree that admit a universal quadratic form defined over $F$. We further obtain several explicit classification results in the case of relative quadratic extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T12:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E12",
      "11E20",
      "11R04",
      "11R80",
      "11H06"
    ],
    "keywords": [
      "general base field",
      "universality lifting",
      "totally real number field",
      "explicit classification results",
      "universal quadratic form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}