{
  "id": "1808.06851",
  "version": "v1",
  "published": "2018-08-21T11:29:27.000Z",
  "updated": "2018-08-21T11:29:27.000Z",
  "title": "Breuil-Mézard conjectures for central division algebras",
  "authors": [
    "Andrea Dotto"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We formulate an analogue of the Breuil-M\\'ezard conjecture for the group of units of a central division algebra over a $p$-adic local field, and we prove that it follows from the conjecture for $\\mathrm{GL}_n$. To do so we construct a transfer of inertial types and Serre weights between the maximal compact subgroups of these two groups, in terms of Deligne-Lusztig theory, and we prove its compatibility with mod $p$ reduction, via the inertial Jacquet-Langlands correspondence and certain explicit character formulas. We also prove analogous statements for $\\ell$-adic coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T11:29:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central division algebra",
      "breuil-mézard conjectures",
      "adic local field",
      "maximal compact subgroups",
      "inertial jacquet-langlands correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}