{
  "id": "1012.0213",
  "version": "v2",
  "published": "2010-12-01T15:18:30.000Z",
  "updated": "2011-06-14T17:18:13.000Z",
  "title": "Geometrization of continuous characters of $\\mathbb{Z}_p^\\times$",
  "authors": [
    "Clifton Cunningham",
    "Masoud Kamgarpour"
  ],
  "comment": "3 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We define the $p$-adic trace of certain rank-one local systems on the multiplicative group over $p$-adic numbers, using Sekiguchi and Suwa's unification of Kummer and Artin-Schrier-Witt theories. Our main observation is that, for every non-negative integer $n$, the $p$-adic trace defines an isomorphism of abelian groups between local systems whose order divides $(p-1)p^n$ and $\\ell$-adic characters of the multiplicative group of $p$-adic integers of depth less than or equal to $n$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-14T17:18:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "14G15"
    ],
    "keywords": [
      "continuous characters",
      "geometrization",
      "multiplicative group",
      "rank-one local systems",
      "adic trace defines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.0213C"
    }
  }
}