{
  "id": "1310.0680",
  "version": "v2",
  "published": "2013-10-02T12:31:57.000Z",
  "updated": "2014-07-21T08:36:51.000Z",
  "title": "Characteristic ideals and Iwasawa theory",
  "authors": [
    "Andrea Bandini",
    "Francesc Bars",
    "Ignazio Longhi"
  ],
  "comment": "15 pages, substantial chenges in exposition, new section 2.3",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let $\\L$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $\\L_d$ and let $M$ be a finitely generated $\\L$-module which is the inverse limit of $\\L_d$-modules $M_d\\,$. Under certain hypotheses on the rings $\\L_d$ and on the modules $M_d\\,$, we define a pro-characteristic ideal for $M$ in $\\L$, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a non-noetherian Iwasawa algebra $\\Z_p[[\\Gal(\\calf/F)]]$, where $F$ is a function field of characteristic $p$ and $\\Gal(\\calf/F)\\simeq\\Z_p^\\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-21T08:36:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "13F25"
    ],
    "keywords": [
      "iwasawa theory",
      "noetherian krull domains",
      "inverse limit",
      "non-noetherian krull domain",
      "usual characteristic ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0680B"
    }
  }
}