{
  "id": "2012.14824",
  "version": "v1",
  "published": "2020-12-29T16:06:50.000Z",
  "updated": "2020-12-29T16:06:50.000Z",
  "title": "Heuristics for $2$-class Towers of Cyclic Cubic Fields",
  "authors": [
    "Nigel Boston",
    "Michael R. Bush"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider the Galois group $G_2(K)$ of the maximal unramified $2$-extension of $K$ where $K/\\mathbb{Q}$ is cyclic of degree $3$. We also consider the group $G^+_2(K)$ where ramification is allowed at infinity. In the spirit of the Cohen-Lenstra heuristics, we identify certain types of pro-$2$ group as the natural spaces where $G_2(K)$ and $G^+_2(K)$ live when the $2$-class group of $K$ is $2$-generated. While we do not have a theoretical scheme for assigning probabilities, we present data and make some observations and conjectures about the distribution of such groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-29T16:06:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R16"
    ],
    "keywords": [
      "cyclic cubic fields",
      "class towers",
      "galois group",
      "cohen-lenstra heuristics",
      "natural spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}