{
  "id": "1602.02592",
  "version": "v1",
  "published": "2016-02-08T14:48:37.000Z",
  "updated": "2016-02-08T14:48:37.000Z",
  "title": "$\\mathfrak{M}_H(G)$-property and congruence of Galois representations",
  "authors": [
    "Meng Fai Lim"
  ],
  "comment": "28 pages; This is a sequel to arXiv:1502.03166 and-at the same time-a partial sequel to arXiv:1409.0942",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the Selmer groups of two congruent Galois representations over an admissible $p$-adic Lie extension. We will show that under appropriate congruence condition, if the dual Selmer group of one satisfies the $\\mathfrak{M}_H(G)$-property, so will the other In the event, the $\\mathfrak{M}_H(G)$-property holds and assuming certain further hypothesis on the decomposition of primes in the $p$-adic Lie extension, we compare the ranks of the $\\pi$-free quotient of the two dual Selmer groups. We then apply our results to study the variation of the dual Selmer groups of specialization of a big Galois representation. We emphasis that our results \\textit{do not} assume the vanishing of the $\\mu$-invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-08T14:48:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R34",
      "11F80"
    ],
    "keywords": [
      "dual selmer group",
      "adic lie extension",
      "congruent galois representations",
      "appropriate congruence condition",
      "big galois representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202592L"
    }
  }
}