{
  "id": "1309.3622",
  "version": "v3",
  "published": "2013-09-14T03:36:28.000Z",
  "updated": "2015-07-03T09:17:27.000Z",
  "title": "On the pseudo-nullity of the dual fine Selmer group",
  "authors": [
    "Meng Fai Lim"
  ],
  "comment": "10 pages; some minor changes",
  "doi": "10.1142/S1793042115500888",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we will study the pseudo-nullity of the fine Selmer group and its related question. Namely, we investigate certain situations, where one can deduce the pseudo-nullity of the dual fine Selmer group of a general Galois module over a admissible $p$-adic Lie extension $F_{\\infty}$ from the knowledge that pseudo-nullity of the Galois group of the maximal abelian unramified pro-$p$ extension of $F_{\\infty}$ at which every prime of $F_{\\infty}$ above $p$ splits completely. In particular, this gives us a way to construct examples of the pseudo-nullity of the dual fine Selmer group of a Galois module that is unramified outside $p$. We will illustrate our results with many examples.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-25T15:20:17.000Z",
      "title": "On the pseudo-nullity of fine Selmer group",
      "abstract": "In this paper, we will study the pseudo-nullity of the fine Selmer group and its related question. Namely, we investigate certain situations, where one can deduce the pseudo-nullity of the dual fine Selmer groups of a general Galois module over a admissible $p$-adic Lie extension $F_{\\infty}$ from the knowledge that pseudo-nullity of the Galois group of the maximal abelian unramified pro-$p$ extension of $F_{\\infty}$ at which every prime of $F_{\\infty}$ above $p$ splits completely. In particular, this gives us a way to construct examples of the pseudo-nullity of the dual fine Selmer group of a Galois module that is unramified outside $p$. We will illustrate our results with many examples.",
      "comment": "9 pages; major reorganization of the presentation; added a new reference",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-07-03T09:17:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R34",
      "11F80"
    ],
    "keywords": [
      "pseudo-nullity",
      "dual fine selmer group",
      "general galois module",
      "adic lie extension",
      "galois group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3622L"
    }
  }
}