{
  "id": "1707.08996",
  "version": "v1",
  "published": "2017-07-27T18:43:49.000Z",
  "updated": "2017-07-27T18:43:49.000Z",
  "title": "One-point covers of elliptic curves and good reduction",
  "authors": [
    "James Phillips"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Raynaud gave a criterion for a branched $G$-cover of curves defined over a mixed-characteristic discretely valued field $K$ with residue characteristic $p$ to have good reduction in the case of either a three-point cover of $\\mathbb{P}^1$ or a one-point cover of an elliptic curve. Specifically, such a cover has potentially good reduction whenever $G$ has a Sylow $p$-subgroup of order $p$ and the absolute ramification index of $K$ is less than the number of conjugacy classes of order $p$ in $G$. In the case of an elliptic curve, we generalize this to the case in which $G$ has an arbitrarily large cyclic Sylow $p$-subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-27T18:43:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "one-point cover",
      "absolute ramification index",
      "arbitrarily large cyclic sylow",
      "three-point cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}