{
  "id": "1603.08640",
  "version": "v1",
  "published": "2016-03-29T04:58:08.000Z",
  "updated": "2016-03-29T04:58:08.000Z",
  "title": "Fine Selmer groups of congruent Galois representations",
  "authors": [
    "Meng Fai Lim"
  ],
  "comment": "14 pages. arXiv admin note: text overlap with arXiv:1602.02592",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the fine Selmer groups of two congruent Galois representations over an admissible $p$-adic Lie extension. We will show that under appropriate congruence conditions, if the dual fine Selmer group of one is pseudo-null, so will the other. In fact, our results also compare the $\\pi$-primary submodules of the two dual fine Selmer groups. We then apply our results to compare the structure of Galois group of the maximal abelian unramified pro-p extension of an admissible $p$-adic Lie extension and the structure of the dual fine Selmer group over the said admissible $p$-adic Lie extension. We also apply our results to compare the structure of the dual fine Selmer groups of various specializations of a big Galois representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-29T04:58:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R34",
      "11F80",
      "16S34"
    ],
    "keywords": [
      "dual fine selmer group",
      "congruent galois representations",
      "adic lie extension",
      "maximal abelian unramified pro-p extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160308640L"
    }
  }
}