{
  "id": "1310.6219",
  "version": "v2",
  "published": "2013-10-23T13:35:34.000Z",
  "updated": "2014-11-20T12:22:51.000Z",
  "title": "The number of varieties in a family which contain a rational point",
  "authors": [
    "Daniel Loughran"
  ],
  "comment": "42 pages. Improved the formatting and the conjectural framework",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-23T13:35:34.000Z",
      "title": "On the number of varieties in a family which contain a rational point",
      "abstract": "We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. A special focus is placed on products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to some special cases of a question posed by Serre on such counting functions. We also speculate about possible generalisations of Serre's problem.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-20T12:22:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11D45",
      "14F22",
      "14M25"
    ],
    "keywords": [
      "rational point",
      "related counting functions",
      "brauer group elements",
      "serres problem",
      "brauer-severi varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6219L"
    }
  }
}