{
  "id": "1612.04549",
  "version": "v1",
  "published": "2016-12-14T09:25:36.000Z",
  "updated": "2016-12-14T09:25:36.000Z",
  "title": "On formal groups and Tate cohomology in local fields",
  "authors": [
    "Nils Ellerbrock",
    "Andreas Nickel"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $L/K$ be a Galois extension of local fields of characteristic $0$ with Galois group $G$. If $\\mathcal{F}$ is a formal group over the ring of integers in $K$, one can associate to $\\mathcal F$ and each positive integer $n$ a $G$-module $F_L^n$ which as a set is the $n$-th power of the maximal ideal of the ring of integers in $L$. We give explicit necessary and sufficient conditions under which $F_L^n$ is a cohomologically trivial $G$-module. This has applications to elliptic curves over local fields and to ray class groups of number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-14T09:25:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local fields",
      "formal group",
      "tate cohomology",
      "ray class groups",
      "galois group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}