{
  "id": "1309.7240",
  "version": "v2",
  "published": "2013-09-27T13:56:05.000Z",
  "updated": "2014-09-08T14:13:17.000Z",
  "title": "On the vanishing of cohomologies of $p$-adic Galois representations associated with elliptic curves",
  "authors": [
    "Jerome T. Dimabayao"
  ],
  "comment": "22 pages, some mistakes fixed, cohomological coprimality introduced, implications in the global setting added",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a $p$-adic field and $E$ an elliptic curve over $K$ with potential good reduction. For some large Galois extensions $L$ of $K$ containing all $p$-power roots of unity, we show the vanishing of certain Galois cohomology groups of $L$ with values in the $p$-adic representation associated with $E$. This generalizes some results of Coates, Sujatha and Wintenberger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-27T13:56:05.000Z",
      "comment": "18 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-08T14:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic galois representations",
      "elliptic curve",
      "large galois extensions",
      "galois cohomology groups",
      "adic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7240D"
    }
  }
}