{
  "id": "1401.7782",
  "version": "v3",
  "published": "2014-01-30T10:12:00.000Z",
  "updated": "2015-08-26T01:28:21.000Z",
  "title": "A cohomological Hasse principle over two-dimensional local rings",
  "authors": [
    "Yong Hu"
  ],
  "comment": "24 pages. v.3: minor changes compared to v2",
  "categories": [
    "math.NT",
    "math.KT"
  ],
  "abstract": "Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$. We use classical machinery from \\'etale cohomology theory, drawing upon an idea in Saito's work on two-dimensional local class field theory. This approach works equally well over the function field of a curve over an equi-characteristic henselian discrete valuation field, thereby giving a different proof of (a slightly generalized version of) a recent result of Harbater, Hartmann and Krashen. We also present two applications. One is the Hasse principle for torsors under quasi-split semisimple simply connected groups without $E_8$ factor. The other gives an explicit upper bound for the Pythagoras number of a Laurent series field in three variables. This bound is sharper than earlier estimates.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-24T08:05:24.000Z",
      "comment": "22 pages. v.2: the claim of novelty of some results in the earlier version is partly inappropriate. Revision made accordingly",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-26T01:28:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E72",
      "11E25",
      "19F15"
    ],
    "keywords": [
      "two-dimensional local rings",
      "cohomological hasse principle",
      "semisimple simply connected groups",
      "equi-characteristic henselian discrete valuation field",
      "two-dimensional local class field theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7782H"
    }
  }
}