{
  "id": "1208.3179",
  "version": "v4",
  "published": "2012-08-15T19:04:24.000Z",
  "updated": "2013-09-18T15:37:37.000Z",
  "title": "The Breuil-Mézard conjecture for potentially Barsotti-Tate representations",
  "authors": [
    "Toby Gee",
    "Mark Kisin"
  ],
  "comment": "Minor expository changes",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the Breuil-M\\'ezard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to the question of determining precise values for the multiplicities that occur). In the case that K/Q_p is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serre's conjecture, proving a variety of results including the Buzzard-Diamond-Jarvis conjecture.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-09-18T15:37:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "potentially barsotti-tate representations",
      "breuil-mézard conjecture",
      "absolute galois group",
      "breuil-mezard conjecture",
      "weight part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3179G"
    }
  }
}