{
  "id": "math/0307095",
  "version": "v1",
  "published": "2003-07-08T16:21:39.000Z",
  "updated": "2003-07-08T16:21:39.000Z",
  "title": "Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M",
  "authors": [
    "Nicolas Ratazzi"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We obtain a lower bound for the normalised height of a non-torsion hypersurface $V$ of a C.M. abelian variety $A$ which is a refinement of a precedent result. This lower bound is optimal in terms of the geometric degree of $V$, up to an absolute power of a ``log'' (independant of the dimension of $A$). We thus extend the results of F. Amoroso and S. David on the same problem on a multiplicative group $\\mathbb{G}_m^n$. When $A$ is an elliptic curve and $V=\\bar{P}$ is the set of conjugates of a non torsion $\\bar{k}$-point, we reobtain the result of M. Laurent on the elliptic Lehmer's problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-08T16:21:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "14G40",
      "14K12",
      "14K22"
    ],
    "keywords": [
      "variétés abéliennes",
      "lehmer pour",
      "lower bound",
      "elliptic lehmers problem",
      "non torsion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4064/aa113-3-5",
      "journal": "Acta Arithmetica",
      "year": 2004,
      "volume": 113,
      "number": 3,
      "pages": 273
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004AcAri.113..273R"
    }
  }
}