{
  "id": "math/0304432",
  "version": "v2",
  "published": "2003-04-27T22:29:05.000Z",
  "updated": "2007-04-30T09:57:35.000Z",
  "title": "Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture",
  "authors": [
    "Luis Dieulefait"
  ],
  "comment": "revised version, to appear in Bol. Soc. Mat. Mexicana",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight $k>3$, \"semistable\" and with multiplicity one, is reducible (for an odd prime $p$),then all the representations in the family are reducible. This, combined with Serre's conjecture (which is now a theorem) gives a proof of the Endoscopy Conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-30T09:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F46"
    ],
    "keywords": [
      "siegel modular forms",
      "endoscopy conjecture",
      "galois representations",
      "uniform behavior",
      "siegel cusp form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4432D"
    }
  }
}