{
  "id": "1512.08264",
  "version": "v1",
  "published": "2015-12-27T19:34:40.000Z",
  "updated": "2015-12-27T19:34:40.000Z",
  "title": "Genus Fields of Congruence Function Fields",
  "authors": [
    "Myriam Maldonado-Ramírez",
    "Martha Rzedowski-Calderón",
    "Gabriel Villa-Salvador"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be a rational congruence function field and consider an arbitrary finite separable extension $K/k$. If for each prime in $k$ ramified in $K$ we have that at least one ramification index is not divided by the characteristic of $K$, we find the genus field $\\g K$, except for constants, of the extension $K/k$. In general, we describe the genus field of a global function field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-27T19:34:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R60",
      "11R58",
      "11R29"
    ],
    "keywords": [
      "genus field",
      "rational congruence function field",
      "global function field",
      "arbitrary finite separable extension",
      "ramification index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208264M"
    }
  }
}