{
  "id": "1607.02602",
  "version": "v1",
  "published": "2016-07-09T12:02:18.000Z",
  "updated": "2016-07-09T12:02:18.000Z",
  "title": "Deformation rings and parabolic induction",
  "authors": [
    "Julien Hauseux",
    "Tobias Schmidt",
    "Claus Sorensen"
  ],
  "comment": "27 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup $P=LN$ defines an isomorphism between the universal deformation rings of a supersingular representation $\\bar{\\sigma}$ of $L$ and of its parabolic induction $\\bar{\\pi}$. As a consequence, we show that every Banach lift of $\\bar{\\pi}$ is induced from a unique Banach lift of $\\bar{\\sigma}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-09T12:02:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "parabolic induction",
      "universal deformation rings",
      "unique banach lift",
      "mild genericity condition",
      "study deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}