{
  "id": "2206.13403",
  "version": "v1",
  "published": "2022-06-27T15:53:06.000Z",
  "updated": "2022-06-27T15:53:06.000Z",
  "title": "Field change for the Cassels-Tate pairing and applications to class groups",
  "authors": [
    "Adam Morgan",
    "Alexander Smith"
  ],
  "comment": "This paper has been split out of the original version of arXiv:2103.08530. 44 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In previous work, the authors defined a category $SMod_F$ of finite Galois modules decorated with local conditions for each global field $F$. In this paper, given an extension $K/F$ of global fields, we define a restriction of scalars functor from $SMod_K$ to $SMod_F$ and show that it behaves well with respect to the Cassels-Tate pairing. We apply this work to study the class groups of global fields in the context of the Cohen-Lenstra heuristics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-27T15:53:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R34",
      "11R29",
      "11R37"
    ],
    "keywords": [
      "class groups",
      "cassels-tate pairing",
      "field change",
      "global field",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}