{
  "id": "0805.1006",
  "version": "v1",
  "published": "2008-05-07T15:59:09.000Z",
  "updated": "2008-05-07T15:59:09.000Z",
  "title": "Admissible unitary completions of locally $Q_p$-rational representations of $GL_2(F)$",
  "authors": [
    "Vytautas Paskunas"
  ],
  "comment": "44 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible unitary completions of certain representations of $GL_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results of Berger, Breuil and Colmez we obtain some results about lifting 2-dimensional mod $p$ representations of the absolute Galois group of $Q_p$ to crystabelline representations with given Hodge-Tate weights.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-07T15:59:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational representations",
      "finite extension",
      "construct admissible unitary completions",
      "absolute galois group",
      "hodge-tate weights"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1006P"
    }
  }
}