{
  "id": "2006.07987",
  "version": "v1",
  "published": "2020-06-14T19:25:00.000Z",
  "updated": "2020-06-14T19:25:00.000Z",
  "title": "High $\\ell$-torsion rank for class groups over function fields",
  "authors": [
    "Iman Setayesh",
    "Jacob Tsimerman"
  ],
  "comment": "5 pages, comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that in the function field setting, $\\ell$-torsion in the class groups of quadratic fields can be arbitrarily large. In fact, we explicitly produce a family whose $\\ell$-rank growth matches the growth in the setting of genus theory, which might be best possible. We do this by specifically focusing on the Artin-Schreir curves $y^2=x^q-x$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-14T19:25:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "class groups",
      "torsion rank",
      "rank growth matches",
      "quadratic fields",
      "genus theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}