{
  "id": "1310.4941",
  "version": "v3",
  "published": "2013-10-18T08:16:12.000Z",
  "updated": "2015-04-23T06:55:02.000Z",
  "title": "Duality for local fields and sheaves on the category of fields",
  "authors": [
    "Takashi Suzuki"
  ],
  "comment": "53 pages. Revised following the referee's comments",
  "categories": [
    "math.NT"
  ],
  "abstract": "Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of this result. We use the category of fields and a Grothendieck topology on it. This simplifies the formulation and proof and reduces the duality to classical results on Galois cohomology. A key point is that the resulting site correctly captures extension groups between algebraic groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-09T08:26:50.000Z",
      "comment": "46 pages. Added a new subsection between 2.4 and 2.5 to correct an error on the treatment of ind-rational algebras. Various parts have been modified accordingly",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-23T06:55:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G45",
      "14F20",
      "13D03"
    ],
    "keywords": [
      "local fields",
      "site correctly captures extension groups",
      "complete discrete valuation fields",
      "finite flat group schemes",
      "perfect residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4941S"
    }
  }
}