{
  "id": "0708.3006",
  "version": "v1",
  "published": "2007-08-22T12:33:02.000Z",
  "updated": "2007-08-22T12:33:02.000Z",
  "title": "Ihara's lemma for imaginary quadratic fields",
  "authors": [
    "Krzysztof Klosin"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "An analogue over imaginary quadratic fields of a result in algebraic number theory known as Ihara's lemma is established. More precisely, we show that for a prime ideal P of the ring of integers of an imaginary quadratic field F, the kernel of the sum of the two standard P-degeneracy maps between the cuspidal sheaf cohomology H^1_!(X_0, M_0)^2 --> H^1_!(X_1, M_1) is Eisenstein. Here X_0 and X_1 are analogues over F of the modular curves X_0(N) and X_0(Np), respectively. To prove our theorem we use the method of modular symbols and the congruence subgroup property for the group SL(2) which is due to Serre.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-22T12:33:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "11F75"
    ],
    "keywords": [
      "imaginary quadratic field",
      "iharas lemma",
      "standard p-degeneracy maps",
      "algebraic number theory",
      "cuspidal sheaf cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3006K"
    }
  }
}