{
  "id": "1407.3589",
  "version": "v2",
  "published": "2014-07-14T10:13:53.000Z",
  "updated": "2014-12-10T09:34:26.000Z",
  "title": "Bad reduction of genus $3$ curves with complex multiplication",
  "authors": [
    "Irene Bouw",
    "Jenny Cooley",
    "Kristin Lauter",
    "Elisa Lorenzo Garcia",
    "Michelle Manes",
    "Rachel Newton",
    "Ekin Ozman"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $C$ be a smooth, absolutely irreducible genus-$3$ curve over a number field $M$. Suppose that the Jacobian of $C$ has complex multiplication by a sextic CM-field $K$. Suppose further that $K$ contains no imaginary quadratic subfield. We give a bound on the primes $\\mathfrak{p}$ of $M$ such that the stable reduction of $C$ at $\\mathfrak{p}$ contains three irreducible components of genus $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-14T10:13:53.000Z",
      "title": "Bad reduction of genus-$3$ curves with complex multiplication",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Irene Bouw",
        "Jenny Cooley",
        "Kristin Lauter",
        "Elisa Lorenzo Garcia",
        "Michella Manes",
        "Rachel Newton",
        "Ekin Ozman"
      ]
    },
    {
      "version": "v2",
      "updated": "2014-12-10T09:34:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G15",
      "14K22",
      "15B33"
    ],
    "keywords": [
      "complex multiplication",
      "bad reduction",
      "imaginary quadratic subfield",
      "number field",
      "sextic cm-field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3589B"
    }
  }
}