{
  "id": "2210.13559",
  "version": "v1",
  "published": "2022-10-24T19:29:24.000Z",
  "updated": "2022-10-24T19:29:24.000Z",
  "title": "A new conjecture on rational points in families",
  "authors": [
    "Daniel Loughran",
    "Nick Rome",
    "Efthymios Sofos"
  ],
  "comment": "47 pages, comments welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of varieties in a family which are everywhere locally soluble.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-24T19:29:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11E20",
      "11D45",
      "14D10",
      "11N36"
    ],
    "keywords": [
      "rational point",
      "conjecture",
      "diagonal planar conics",
      "serres problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}