{
  "id": "1309.1600",
  "version": "v2",
  "published": "2013-09-06T11:04:25.000Z",
  "updated": "2016-08-04T13:33:42.000Z",
  "title": "Local deformation rings and a Breuil-Mézard conjecture when l\\neq p",
  "authors": [
    "Jack Shotton"
  ],
  "comment": "35 pages. To appear in Algebra and Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) an analogue of the Breuil-M\\'{e}zard conjecture holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL_2(O_F).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-06T11:04:25.000Z",
      "abstract": "We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) an analogue of the Breuil-M\\'{e}zard conjecture of holds, relating the special fibres of these deformation rings to the mod l reduction of certain irreducible representations of GL_2(O_F).",
      "comment": "23 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-08-04T13:33:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S37"
    ],
    "keywords": [
      "local deformation rings",
      "breuil-mézard conjecture",
      "special fibres",
      "fixed inertial type",
      "dimensional mod"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1600S"
    }
  }
}