{
  "id": "0710.1053",
  "version": "v3",
  "published": "2007-10-04T16:45:33.000Z",
  "updated": "2010-01-05T16:55:32.000Z",
  "title": "Extensions for supersingular representations of $GL_2(Q_p)$",
  "authors": [
    "Vytautas Paskunas"
  ],
  "comment": "This version contains more details. Sections 3 and 9 containing some background information are new. An appendix is added",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $p>2$ be a prime number. Let $G:=GL_2(Q_p)$ and $\\pi$, $\\tau$ smooth irreducible representations of $G$ on $\\bar{F}_p$-vector spaces with a central character. We show if $\\pi$ is supersingular then $Ext^1_G(\\tau,\\pi)\\neq 0$ implies $\\tau\\cong \\pi$. This answers affirmatively for $p>2$ a question of Colmez. We also determine $Ext^1_G(\\tau,\\pi)$, when $\\pi$ is the Steinberg representation. As a consequence of our results combined with those already in the literature one knows $Ext^1_G(\\tau,\\pi)$ for all irreducible representations of $G$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-05T16:55:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersingular representations",
      "extensions",
      "steinberg representation",
      "central character",
      "smooth irreducible representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1053P"
    }
  }
}