{
  "id": "0804.4153",
  "version": "v1",
  "published": "2008-04-25T17:33:02.000Z",
  "updated": "2008-04-25T17:33:02.000Z",
  "title": "The Other Group of as Galois Extension",
  "authors": [
    "Lex E. Renner"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k\\subseteq K$ be a finite Galois extension of fields with Galois group $G$. Let $\\mathscr{G}$ be the automorphism $k$-group scheme of $K$. We construct a canonical $k$-subgroup scheme $\\underline{G}\\subset\\mathscr{G}$ with the property that $Spec_k(K)$ is a $k$-torsor for $\\underline{G}$. $\\underline{G}$ is a constant $k$-group if and only if $G$ is abelian, in which case $G=\\underline{G}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-25T17:33:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F10"
    ],
    "keywords": [
      "finite galois extension",
      "galois group",
      "subgroup scheme",
      "automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4153R"
    }
  }
}