{
  "id": "math/0701177",
  "version": "v1",
  "published": "2007-01-05T20:44:15.000Z",
  "updated": "2007-01-05T20:44:15.000Z",
  "title": "An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters",
  "authors": [
    "Tobias Berger"
  ],
  "comment": "26 pages",
  "journal": "Compos. Math. 145 (2009), no. 3, 603--632",
  "doi": "10.1112/S0010437X09003984",
  "categories": [
    "math.NT"
  ],
  "abstract": "For certain algebraic Hecke characters chi of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL_2/F. By finding congruences between Eisenstein cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms of the special L-value L(0,chi). We further prove that its index is bounded from above by the order of the Selmer group of the p-adic Galois character associated to chi^{-1}. This uses the work of R. Taylor et al. on attaching Galois representations to cuspforms of GL_2/F. Together these results imply a lower bound for the size of the Selmer group in terms of L(0,chi), coinciding with the value given by the Bloch-Kato conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-05T20:44:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F33",
      "11F75"
    ],
    "keywords": [
      "imaginary quadratic field",
      "eisenstein ideal",
      "bloch-kato conjecture",
      "lower bound",
      "selmer group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1177B"
    }
  }
}