{
  "id": "1910.11636",
  "version": "v1",
  "published": "2019-10-25T11:50:06.000Z",
  "updated": "2019-10-25T11:50:06.000Z",
  "title": "Fields Generated by Finite Rank Subgroups of Tori and Elliptic Curves",
  "authors": [
    "Lukas Pottmeyer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Gamma$ be a finite rank subgroup of $G$, where $G$ is either the linear torus or an CM-elliptic curve defined over a number field. We prove that the group of points in $G$ which are rational over the field generated by all elements in the divisible hull of $\\Gamma$, is free abelian modulo this divisible hull. This proves that a necessary condition for R\\'emond's generalized Lehmer conjecture is satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-25T11:50:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11G05",
      "20K15"
    ],
    "keywords": [
      "finite rank subgroup",
      "elliptic curves",
      "free abelian modulo",
      "divisible hull",
      "remonds generalized lehmer conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}