{
  "id": "1710.03635",
  "version": "v1",
  "published": "2017-10-10T14:53:36.000Z",
  "updated": "2017-10-10T14:53:36.000Z",
  "title": "Local-global Galois theory of arithmetic function fields",
  "authors": [
    "David Harbater",
    "Julia Hartmann",
    "Daniel Krashen",
    "R. Parimala",
    "V. Suresh"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RA",
    "math.AG",
    "math.NT"
  ],
  "abstract": "We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the local absolute Galois group to inject into the global absolute Galois group. As an application we obtain a local-global principle for the index of a variety over such a function field. In this context we also study algebraic versions of van Kampen's theorem, describing the global absolute Galois group as a pushout of local absolute Galois groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T14:53:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F10",
      "13F25",
      "14H25",
      "13B05",
      "14H05",
      "20E18"
    ],
    "keywords": [
      "arithmetic function fields",
      "local-global galois theory",
      "global absolute galois group",
      "local absolute galois group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}