{
  "id": "0906.4626",
  "version": "v2",
  "published": "2009-06-25T08:26:40.000Z",
  "updated": "2009-12-27T15:11:59.000Z",
  "title": "The genus fields of Artin-Schreier extensions",
  "authors": [
    "Su Hu",
    "Yan Li"
  ],
  "comment": "9 pages, Corrected typos",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $q$ be a power of a prime number $p$. Let $k=\\mathbb{F}_{q}(t)$ be the rational function field with constant field $\\mathbb{F}_{q}$. Let $K=k(\\alpha)$ be an Artin-Schreier extension of $k$. In this paper, we explicitly describe the ambiguous ideal classes and the genus field of $K$ . Using these results we study the $p$-part of the ideal class group of the integral closure of $\\mathbb{F}_{q}[t]$ in $K$. And we also give an analogy of R$\\acute{e}$dei-Reichardt's formulae for $K$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-27T15:11:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R58"
    ],
    "keywords": [
      "genus field",
      "artin-schreier extension",
      "ideal class group",
      "rational function field",
      "dei-reichardts formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4626H"
    }
  }
}