{
  "id": "math/0307031",
  "version": "v1",
  "published": "2003-07-02T14:42:01.000Z",
  "updated": "2003-07-02T14:42:01.000Z",
  "title": "Automorphisms groups for $p$-cyclic covers of the affine line",
  "authors": [
    "Claus Lehr",
    "Michel Matignon"
  ],
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $k$ be an algebraically closed field of positive characteristic $p>0$ and $C \\to {\\mathbb P}^1_k$ a $p$-cyclic cover of the projective line ramified in exactly one point. We are interested in the $p$-part of the full automorphism group $Aut_k C$. First we prove that these groups are exactly the extra-special $p$-groups and groups G which are subgroups of an extra-special group E such that $Z(E) \\subseteq G$. The paper also describes an efficient algorithm to compute the $p$-part of $\\Aut_k C$ starting from an Artin-Schreier equation for the cover $C \\to {\\mathbb P}^1_k$. The interest for these objects initially came from the study of the stable reduction of $p$-cyclic covers over the $p$-adics. There the covers $C \\to {\\mathbb P}^1_k$ naturally arise and their automorphism groups play a major role in understanding the arithmetic monodromy. Our methods rely on previous work by Stichtenoth whose approach we have adopted.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-02T14:42:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14H30",
      "14Q05"
    ],
    "keywords": [
      "cyclic cover",
      "automorphisms groups",
      "affine line",
      "automorphism groups play",
      "full automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7031L"
    }
  }
}