{
  "id": "1405.0896",
  "version": "v2",
  "published": "2014-05-05T13:44:32.000Z",
  "updated": "2014-12-21T04:42:25.000Z",
  "title": "Trace of abelian varieties over function fields and the geometric Bogomolov conjecture",
  "authors": [
    "Kazuhiko Yamaki"
  ],
  "comment": "27 pages. There is an appendix added, which is used in the proof of Proposition 4.6. There was an error in Lemma 4.7, which has been resolved in this revision",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety. To prove the results, we investigate closed subvarieties of abelian schemes over constant varieties, where constant varieties are varieties over a function field which can be defined over the constant field of the function field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-05T13:44:32.000Z",
      "title": "Subvarieties of abelian schemes over constant varieties and the geometric Bogomolov conjecture",
      "abstract": "In this paper, we investigate closed subvarieties of abelian schemes over constant varieties and contribute to the geometric Bogomolov conjecture for abelian varieties. We prove, in fact, that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, we see that the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety.",
      "comment": "25 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-21T04:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian schemes",
      "constant varieties",
      "geometric bogomolov conjecture holds",
      "degenerate abelian varieties",
      "constant abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0896Y"
    }
  }
}