{
  "id": "1909.06725",
  "version": "v1",
  "published": "2019-09-15T03:42:36.000Z",
  "updated": "2019-09-15T03:42:36.000Z",
  "title": "On a relation of overconvergence and $F$-analyticity on $p$-adic Galois representations of a $p$-adic field $F$",
  "authors": [
    "Megumi Takata"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime number. There are properties called ``overconvergence'' and ``$F$-analyticity'' for $p$-adic Galois representations of a $p$-adic field $F$. By Berger's work, it is known that $F$-analyticity is stricter than overconvergence. In this article, we show that, in many cases, an overconvergent Galois representation is $F$-analytic up to a twist by a character. This result emphasizes the necessity of the theory of $(\\varphi,\\Gamma)$-modules over the multivariable Robba ring, by which we expect to study all $p$-adic Galois representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-15T03:42:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S20",
      "11S31"
    ],
    "keywords": [
      "adic galois representations",
      "adic field",
      "analyticity",
      "overconvergence",
      "overconvergent galois representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}