{
  "id": "math/0408167",
  "version": "v3",
  "published": "2004-08-12T14:36:37.000Z",
  "updated": "2010-09-03T22:56:23.000Z",
  "title": "Companion forms over totally real fields",
  "authors": [
    "Toby Gee"
  ],
  "comment": "Appeared as Manuscripta Math. 125 (2008), no. 1, 1-41. This version does not incorporate any minor changes (e.g. typographical changes) made in proof",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that if F is a totally real field in which p splits completely and f is a mod p Hilbert modular form with parallel weight 2<k<p, which is totally ordinary at p and has tamely ramified Galois representation at all primes dividing p, then there is a \"companion form\" of parallel weight k':=p+1-k. This work generalises results of Gross and Coleman-Voloch for modular forms over Q.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-09-03T22:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41"
    ],
    "keywords": [
      "totally real field",
      "companion form",
      "parallel weight",
      "hilbert modular form",
      "work generalises results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8167G"
    }
  }
}