{
  "id": "1209.5309",
  "version": "v3",
  "published": "2012-09-24T15:45:24.000Z",
  "updated": "2013-07-04T12:48:44.000Z",
  "title": "Minimal modularity lifting for GL2 over an arbitrary number field",
  "authors": [
    "David Hansen"
  ],
  "comment": "8 pages; final version, to appear in Math. Res. Letters",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "We prove a modularity lifting theorem for minimally ramified deformations of two-dimensional odd Galois representations, over an arbitrary number field. The main ingredient is a generalization of the Taylor-Wiles method in which we patch complexes rather than modules.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-04T12:48:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary number field",
      "minimal modularity lifting",
      "two-dimensional odd galois representations",
      "main ingredient",
      "modularity lifting theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5309H"
    }
  }
}