{
  "id": "1705.08175",
  "version": "v1",
  "published": "2017-05-23T10:52:34.000Z",
  "updated": "2017-05-23T10:52:34.000Z",
  "title": "The Galois group of the category of mixed Hodge-Tate structures",
  "authors": [
    "Alexander Goncharov",
    "Guangyu Zhu"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The category of rational mixed Hodge-Tate structures is a mixed Tate category. Therefore thanks to the Tannakian formalism, it is equivalent to the category of finite dimensional graded comodules over a graded commutative Hopf algebra H over Q. Since the category has homological dimension 1, the Hopf algebra H is isomorphic to the commutative graded Hopf algebra provided by the tensor algebra of the graded vector space given by the direct sum of the groups C/Q(n) over n>0. However this isomorphism is not natural in any sense, e.g. does not work in families. We give a different natural explicit construction of the Hopf algebra H.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-23T10:52:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois group",
      "finite dimensional graded comodules",
      "rational mixed hodge-tate structures",
      "natural explicit construction",
      "commutative graded hopf algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}