{
  "id": "1608.04181",
  "version": "v1",
  "published": "2016-08-15T05:31:54.000Z",
  "updated": "2016-08-15T05:31:54.000Z",
  "title": "$\\F_p$-representations over $p$-fields",
  "authors": [
    "Chandan Singh Dalawat"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime, $k$ a finite extension of $\\F_p$ of cardinal $q$, $l$ a finite extension of $k$ of group $\\Sigma=\\Gal(l|k)$, and $T$ a subgroup of $l^\\times$. Using the method of \"\\thinspace little groups\\thinspace\", we classify irreducible $\\F_p$-representations of the group $G=T\\times_q\\Sigma$, the twisted product of $\\Sigma$ with the $\\Sigma$-module $T$. We then use these results to classify irreducible continuous $\\F_p$-representations of the profinite group of automorphisms $\\Gal(\\tilde K|K)$ of the maximal galoisian extension $\\tilde K$ of a local field $K$ with residue field~$k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-15T05:31:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11S99",
      "20C20"
    ],
    "keywords": [
      "representations",
      "finite extension",
      "maximal galoisian extension",
      "local field",
      "profinite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}