{
  "id": "1212.3465",
  "version": "v2",
  "published": "2012-12-14T13:22:03.000Z",
  "updated": "2014-03-18T11:08:25.000Z",
  "title": "Recursive towers of curves over finite fields using graph theory",
  "authors": [
    "Emmanuel Hallouin",
    "Marc Perret"
  ],
  "comment": "31 pages, 3 figures",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give a new way to study recursive towers of curves over a finite field, defined from a bottom curve $\\Cun$ and a correspondence $\\Cdeux$ on $\\Cun$.In particular, we study their asymptotic behavior. A close examination of singularities leads to a necessary condition for a tower to be asymptotically good. Then, spectral theory on a directed graph and considerations on the class of $\\Cdeux$ in $\\NS (\\Cun \\times \\Cun)$ lead to the fact that, under some mild assumptions, a recursive tower which does not reach Drinfeld-Vladut bound cannot be optimal in Tsfasmann-Vladut sense. Results are applied to the Bezerra-Garcia-Stichtenoth tower along the paper for illustration.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-18T11:08:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14G05",
      "14G15",
      "14H20"
    ],
    "keywords": [
      "finite field",
      "graph theory",
      "reach drinfeld-vladut bound",
      "tsfasmann-vladut sense",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3465H"
    }
  }
}