{
  "id": "0807.1078",
  "version": "v3",
  "published": "2008-07-07T18:21:28.000Z",
  "updated": "2009-02-26T16:23:58.000Z",
  "title": "Crystalline representations of G_Qp^a with coefficients",
  "authors": [
    "Hui June Zhu"
  ],
  "comment": "37 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This paper studies crystalline representations of G_K with coefficients of any dimension, where K is the unramified extension of Q_p of degree a. We prove a theorem of Fontaine-Laffaille type when \\sigma-invariant Hodge-Tate weight less than p-1, which establishes the bijection between Galois stable lattices in crystalline representations and strongly divisible \\phi-lattice. In generalizing Breuil's work, we classify all reducible and irreducible crystalline representations of G_K of dimensional 2, then describe their mod p reductions. We generalize some results (of Deligne, Fontaine-Serre, and Edixhoven) to representations arising from Hilbert modular forms when \\sigma-invariant Hodge-Tate weight less than p-1.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-02-26T16:23:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11-xx",
      "14-xx"
    ],
    "keywords": [
      "coefficients",
      "hodge-tate weight",
      "paper studies crystalline representations",
      "hilbert modular forms",
      "galois stable lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.1078Z"
    }
  }
}