{
  "id": "math/0606531",
  "version": "v2",
  "published": "2006-06-21T16:30:21.000Z",
  "updated": "2007-01-05T18:54:14.000Z",
  "title": "Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields",
  "authors": [
    "Tobias Berger"
  ],
  "comment": "37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introduction",
  "journal": "Manuscripta Math. 125 (2008), no. 4, 427--470",
  "doi": "10.1007/s00229-007-0139-6",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-05T18:54:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "11F67",
      "22E41"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "eisenstein cohomology classes",
      "denominator",
      "special l-value",
      "hecke character"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6531B"
    }
  }
}