{
  "id": "math/0411291",
  "version": "v1",
  "published": "2004-11-12T16:25:11.000Z",
  "updated": "2004-11-12T16:25:11.000Z",
  "title": "On the Manin-Mumford conjecture for abelian varieties with a prime of supersingular reduction",
  "authors": [
    "Tetsushi Ito"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give a short proof of the \"prime-to-$p$ version\" of the Manin-Mumford conjecture for an abelian variety over a number field, when it has supersingular reduction at a prime dividing $p$, by combining the methods of Bogomolov, Hrushovski, and Pink-Roessler. Our proof here is quite simple and short, and neither $p$-adic Hodge theory nor model theory is used. The observation is that a power of a lift of the Frobenius element at a supersingular prime acts on the prime-to-$p$ torsion points via nontrivial homothety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-11-12T16:25:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K12",
      "11G10",
      "14G15"
    ],
    "keywords": [
      "abelian variety",
      "supersingular reduction",
      "manin-mumford conjecture",
      "adic hodge theory",
      "supersingular prime acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11291I"
    }
  }
}