{
  "id": "2204.01874",
  "version": "v1",
  "published": "2022-04-04T22:34:15.000Z",
  "updated": "2022-04-04T22:34:15.000Z",
  "title": "Function field genus theory for non-Kummer extensions",
  "authors": [
    "Martha Rzedowski-Calderón",
    "Gabriel Villa-Salvador"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we first obtain the genus field of a finite abelian non-Kummer $l$--extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields and our previous results, we deduce the general expression of the genus field of a finite abelian extension of a global rational function field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-04T22:34:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R58",
      "11R29",
      "11R60"
    ],
    "keywords": [
      "function field genus theory",
      "global rational function field",
      "non-kummer extensions",
      "genus field",
      "finite abelian extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}