{
  "id": "math/0609387",
  "version": "v2",
  "published": "2006-09-14T09:09:24.000Z",
  "updated": "2007-02-06T13:39:16.000Z",
  "title": "The Bogomolov conjecture for totally degenerate abelian varieties",
  "authors": [
    "Walter Gubler"
  ],
  "comment": "21 pages; submitted. Minor errors corrected, applications in Section 6 added",
  "journal": "Invent. Math. 169, No.2, 377-400 (2007)",
  "doi": "10.1007/s00222-007-0049-y",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove the Bogomolov conjecture for an abelian variety A over a function field which is totally degenerate at a place v. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place. As an application, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-06T13:39:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40",
      "11G10"
    ],
    "keywords": [
      "abelian variety",
      "totally degenerate abelian varieties",
      "bogomolov conjecture",
      "adapt zhangs proof",
      "maximal unramified algebraic extension"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2007,
      "month": "Apr",
      "volume": 169,
      "number": 2,
      "pages": 377
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InMat.169..377G"
    }
  }
}