{
  "id": "math/0610488",
  "version": "v2",
  "published": "2006-10-16T14:58:52.000Z",
  "updated": "2007-12-30T05:25:04.000Z",
  "title": "Weights in Serre's conjecture for Hilbert modular forms: the ramified case",
  "authors": [
    "Michael M. Schein"
  ],
  "comment": "Notation improved and typos corrected; to appear in Israel J. Math",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which r is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which supposed that p was unramified in F. We also prove a theorem towards the conjecture and provide some computational evidence.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-30T05:25:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80"
    ],
    "keywords": [
      "hilbert modular forms",
      "serres conjecture",
      "ramified case",
      "absolute galois group",
      "odd prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10488S"
    }
  }
}