{
  "id": "1010.0152",
  "version": "v2",
  "published": "2010-10-01T13:16:30.000Z",
  "updated": "2011-02-17T16:13:54.000Z",
  "title": "The average rank of elliptic $n$-folds",
  "authors": [
    "Remke Kloosterman"
  ],
  "comment": "Expansion of the discussion of the cycle class map; several minor changes",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $V/\\mathbb{F}_q$ be a variety of dimension at least two. We show that the density of elliptic curves $E/\\mathbb{F}_q(V)$ with positive rank is zero if $V$ has dimension at least 3 and is at most $1-\\zeta_V(3)^{-1}$ if $V$ is a surface.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-17T16:13:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average rank",
      "elliptic curves",
      "positive rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.0152K"
    }
  }
}