{
  "id": "1208.0583",
  "version": "v5",
  "published": "2012-08-02T19:43:52.000Z",
  "updated": "2015-01-23T22:32:35.000Z",
  "title": "Commuting-Liftable Subgroups of Galois Groups II",
  "authors": [
    "Adam Topaz"
  ],
  "comment": "62 pages; final version; NOTE: numbering has changed from previous versions",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $n$ denote either a positive integer or $\\infty$, let $\\ell$ be a fixed prime and let $K$ be a field of characteristic different from $\\ell$. In the presence of sufficiently many roots of unity in $K$, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal $\\ell^n$-abelian Galois group of $K$ using the maximal $\\ell^N$-abelian-by-central Galois group of $K$, whenever $N$ is sufficiently large relative to $n$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-03-07T19:07:40.000Z",
      "abstract": "Let n denote either a positive integer or infinity, let \\ell be a fixed prime and let K be a field of characteristic different from \\ell. In the presence of sufficiently many roots of unity in K, we show how to recover some of the inertia/decomposition structure of valuations inside the maximal (Z/\\ell^n)-abelian Galois group (resp. pro-\\ell-abelian Galois group) of K using the maximal (Z/\\ell^N)-abelian-by-central Galois group (resp. pro-\\ell-abelian-by-central Galois group) of K, whenever N is sufficiently large relative to n.",
      "comment": "47 pages; fixed several typos; fixed minor error in Example 4.3",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-01-23T22:32:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12E30",
      "12F10",
      "12G05",
      "12J25"
    ],
    "keywords": [
      "galois group",
      "commuting-liftable subgroups",
      "inertia/decomposition structure",
      "valuations inside",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.0583T"
    }
  }
}