{
  "id": "1604.04571",
  "version": "v1",
  "published": "2016-04-15T17:06:28.000Z",
  "updated": "2016-04-15T17:06:28.000Z",
  "title": "Level structures on abelian varieties and Vojta's conjecture",
  "authors": [
    "Dan Abramovich",
    "Keerthi Madapusi Pera",
    "Anthony Várilly-Alvarado"
  ],
  "comment": "Appendix by Keerthi Madapusi Pera. 26 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Assuming Vojta's conjecture, and building on recent work of the authors, we prove that, for a fixed number field $K$ and positive integer $g$, there is an integer $m_0$ such that for any $m > m_0$ there is no principally polarized abelian variety $A/K$ of dimension $g$ with full level-$m$ structure. To this end, we develop a version of Vojta's conjecture for Deligne-Mumford stacks, which we deduce from Vojta's conjecture for schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T17:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K10",
      "14K15",
      "11G35",
      "11G18"
    ],
    "keywords": [
      "level structures",
      "deligne-mumford stacks",
      "assuming vojtas conjecture",
      "fixed number field",
      "principally polarized abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404571A"
    }
  }
}