{
  "id": "1504.00148",
  "version": "v1",
  "published": "2015-04-01T08:49:57.000Z",
  "updated": "2015-04-01T08:49:57.000Z",
  "title": "Reductions of Galois representations for slopes in $(1,2)$",
  "authors": [
    "Shalini Bhattacharya",
    "Eknath Ghate"
  ],
  "comment": "41 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe the semi-simplification of the mod $p$ reduction of certain crystalline two dimensional local Galois representations of slopes in the interval $(1,2)$ and all weights. The proof uses the mod $p$ Local Langlands Correspondence for $GL_2(Q_p)$. We also give a complete description of the submodules generated by the second highest monomial in the mod $p$ symmetric power representations of $GL_2(F_p)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-01T08:49:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80"
    ],
    "keywords": [
      "dimensional local galois representations",
      "local langlands correspondence",
      "second highest monomial",
      "symmetric power representations",
      "complete description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}