{
  "id": "1604.05822",
  "version": "v1",
  "published": "2016-04-20T05:30:51.000Z",
  "updated": "2016-04-20T05:30:51.000Z",
  "title": "Deformations of Galois representations and exceptional monodromy, II: raising the level",
  "authors": [
    "Stefan Patrikis"
  ],
  "comment": "comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Building on lifting results of Ramakrishna, Khare and Ramakrishna proved a purely Galois-theoretic level-raising theorem for two-dimensional odd representations of the Galois group of Q. In this paper, we generalize these techniques from type A1 to general (semi-)simple groups. We then strengthen our previous results on constructing geometric Galois representations with exceptional monodromy groups, achieving such constructions for almost all l, rather than a density-one set, and achieving greater flexibility in the Hodge numbers of the lifts; the latter improvement requires the new level-raising result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-20T05:30:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformations",
      "constructing geometric galois representations",
      "exceptional monodromy groups",
      "two-dimensional odd representations",
      "ramakrishna"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}