{
  "id": "1204.0383",
  "version": "v2",
  "published": "2012-04-02T12:17:48.000Z",
  "updated": "2013-11-04T12:15:51.000Z",
  "title": "Counting rational points over number fields on a singular cubic surface",
  "authors": [
    "Christopher Frei"
  ],
  "comment": "22 pages, 1 figure; minor revision",
  "journal": "Algebra Number Theory 7 (6): 1451-1479, 2013",
  "doi": "10.2140/ant.2013.7-6",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin's conjecture over the field Q of rational numbers. Combining this method with techniques developed by Schanuel, we give a proof of Manin's conjecture over arbitrary number fields for the singular cubic surface S given by the equation w^3 = x y z.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-04T12:15:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "14G05"
    ],
    "keywords": [
      "singular cubic surface",
      "counting rational points",
      "manins conjecture",
      "hard special cases",
      "arbitrary number fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0383F"
    }
  }
}