{
  "id": "1006.0466",
  "version": "v1",
  "published": "2010-06-02T18:56:39.000Z",
  "updated": "2010-06-02T18:56:39.000Z",
  "title": "Congruences between Hilbert modular forms: constructing ordinary lifts",
  "authors": [
    "Thomas Barnet-Lamb",
    "Toby Gee",
    "David Geraghty"
  ],
  "comment": "48 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that r|_{G_F'} has a modular lift which is ordinary at each place dividing l. We deduce a similar result for r itself, under the assumption that at places v|l the representation r|_{G_F_v} is reducible. This allows us to deduce improvements to results in the literature on modularity lifting theorems for potentially Barsotti-Tate representations and the Buzzard-Diamond-Jarvis conjecture. The proof makes use of a novel lifting technique, going via rank 4 unitary groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-02T18:56:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33"
    ],
    "keywords": [
      "hilbert modular forms",
      "constructing ordinary lifts",
      "congruences",
      "finite solvable totally real extension",
      "algebraic closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0466B"
    }
  }
}