{
  "id": "0912.4017",
  "version": "v1",
  "published": "2009-12-21T12:34:42.000Z",
  "updated": "2009-12-21T12:34:42.000Z",
  "title": "Algebraic Anabelian Functors",
  "authors": [
    "Feng-Wen An"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this paper we will prove that there exists a covariant functor, called algebraic anabelian functor, from the category of algebraic schemes over a given field to the category of outer homomorphism sets of groups. The algebraic anabelian functor, given in a canonical manner, is full and faithful. It reformulates the anabelian geometry over a field. As an application of the anabelian functor, we will also give a proof of the section conjecture of Grothendieck for the case of algebraic schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-21T12:34:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "11G35"
    ],
    "keywords": [
      "algebraic anabelian functor",
      "algebraic schemes",
      "outer homomorphism sets",
      "section conjecture",
      "covariant functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.4017A"
    }
  }
}