{
  "id": "math/0703882",
  "version": "v1",
  "published": "2007-03-29T14:14:47.000Z",
  "updated": "2007-03-29T14:14:47.000Z",
  "title": "On Jannsen's conjecture for Hecke characters of imaginary quadratic fields",
  "authors": [
    "Francesc Bars"
  ],
  "comment": "To appear in Proceedings of the Primeras Jornadas de Teoria de Numeros",
  "categories": [
    "math.NT"
  ],
  "abstract": "We present a collection of results on a conjecture of Jannsen about the $p$-adic realizations associated to Hecke characters over an imaginary quadratic field $K$ of class number 1. The conjecture is easy to check for Galois groups purely of local type. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field $K$ at $p$, which is related to the property that a global Galois group is purely of local type. Without this regularity assumption at $p$, we present a review of the known situations in the critical case and in the non-critical case for the realizations associated to Hecke characters over $K$. We relate the conjecture to the non-vanishing of some concrete non-critical values of the associated $p$-adic $L$-function of the Hecke character. Finally, we prove that the conjecture follows from a general conjecture on Iwasawa theory for almost all Tate twists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-29T14:14:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "11R34",
      "14F20",
      "19F27",
      "11R23"
    ],
    "keywords": [
      "imaginary quadratic field",
      "hecke character",
      "jannsens conjecture",
      "local type",
      "geometric regularity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3882B"
    }
  }
}