{
  "id": "1708.01782",
  "version": "v1",
  "published": "2017-08-05T15:42:55.000Z",
  "updated": "2017-08-05T15:42:55.000Z",
  "title": "Hyperbolicity over function fields of quadrics",
  "authors": [
    "James O'Shea"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of important established results in quadratic form theory by means of novel, short and elementary proofs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-05T15:42:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E04",
      "11E16",
      "11E81",
      "12F20",
      "14E05"
    ],
    "keywords": [
      "function field",
      "hyperbolicity",
      "quadratic form theory",
      "strong consequence",
      "important established results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}