{
  "id": "0710.2549",
  "version": "v1",
  "published": "2007-10-12T20:51:39.000Z",
  "updated": "2007-10-12T20:51:39.000Z",
  "title": "Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture",
  "authors": [
    "Krzysztof Klosin"
  ],
  "comment": "57 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let k be a positive integer divisible by 4, l>k a prime, and f an elliptic cuspidal eigenform of weight k-1, level 4, and non-trivial character. Let \\rho_f be the l-adic Galois representation attached to f. In this paper we provide evidence for the Bloch-Kato conjecture for a twist of the adjoint motif of \\rho_f in the following way. Let L(f,s) denote the symmetric square L-function of f. We prove that (under certain conditions) the l-adic valuation of the algebraic part of L(f, k) is no greater than the l-adic valuation of the order of S, where S is (the Pontryagin dual of) the Selmer group attached to the Galois module \\ad^0\\rho_f|_{G_K} (-1), and K= Q(i). Our method uses an idea of Ribet in that we introduce an intermediate step and produce congruences between CAP and non-CAP modular forms on the unitary group U(2,2).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-12T20:51:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F55",
      "11F67",
      "11F80"
    ],
    "keywords": [
      "bloch-kato conjecture",
      "l-adic valuation",
      "elliptic cuspidal eigenform",
      "symmetric square l-function",
      "non-cap modular forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2549K"
    }
  }
}