{
  "id": "1405.6371",
  "version": "v2",
  "published": "2014-05-25T10:34:07.000Z",
  "updated": "2014-09-18T17:47:17.000Z",
  "title": "Sur une conjecture de Breuil-Herzig",
  "authors": [
    "Julien Hauseux"
  ],
  "comment": "theorem 4.1.2 is a slight generalization of proposition 4.1.2 in v1, minor corrections in the proofs of subsection 3.2, 42 pages, in French",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove a conjecture of Breuil and Herzig on the uniqueness of certain unitary continuous representations of a $p$-adic reductive group whose constituents are principal series. In order to do so, we partially compute Emerton's $\\delta$-functor $\\mathrm{H^\\bullet Ord}_P$ of derived ordinary parts with respect to a parabolic subgroup on a principal series. We formulate a new conjecture on the extensions between admissible smooth mod $p$ representations of a $p$-adic reductive group and we prove it in the case of extensions by a principal series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-25T10:34:07.000Z",
      "abstract": "We prove the conjecture of Breuil and Herzig on the uniqueness of certain unitary continuous representations of a $p$-adic reductive group whose constituents are principal series. In order to do so, we compute Emerton's $\\delta$-functor $\\mathrm{H^\\bullet Ord}_P$ on a principal series. We formulate a new conjecture on the extensions between admissible smooth mod $p$ representations of a $p$-adic reductive group and we prove it in the case of extensions by a principal series.",
      "comment": "41 pages, in French",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-18T17:47:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "conjecture",
      "principal series",
      "adic reductive group",
      "breuil-herzig",
      "unitary continuous representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6371H"
    }
  }
}