{
  "id": "0808.1038",
  "version": "v1",
  "published": "2008-08-07T14:37:14.000Z",
  "updated": "2008-08-07T14:37:14.000Z",
  "title": "A Banach space determined by the Weil height",
  "authors": [
    "Daniel Allcock",
    "Jeffrey D. Vaaler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The absolute logarithmic Weil height is well defined on the group of units of the algebraic closure of the rational numbers, modulo roots of unity, and induces a metric topology on this group. We show that the completion of this metric space is a Banach space over the field of real numbers. We further show that this Banach space is isometrically isomorphic to a co-dimension one subspace of L1 of a certain totally disconnected, locally compact space, equipped with a certain measure satisfying an invariance property with respect to the absolute Galois group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-07T14:37:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J25",
      "11R04"
    ],
    "keywords": [
      "banach space",
      "absolute logarithmic weil height",
      "absolute galois group",
      "invariance property",
      "algebraic closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}