{
  "id": "1405.7380",
  "version": "v1",
  "published": "2014-05-28T20:01:06.000Z",
  "updated": "2014-05-28T20:01:06.000Z",
  "title": "Zeta Functions of Curves with no Rational Points",
  "authors": [
    "Daniel Litt"
  ],
  "comment": "12 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We show that the motivic zeta functions of smooth, geometrically connected curves with no rational points are rational functions. This was previously known only for curves whose smooth projective models have a rational point on each connected component. In the course of the proof we study the class of a Severi-Brauer scheme over a general base in the Grothendieck ring of varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-28T20:01:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational point",
      "motivic zeta functions",
      "rational functions",
      "smooth projective models",
      "severi-brauer scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7380L"
    }
  }
}