{
  "id": "1711.06456",
  "version": "v1",
  "published": "2017-11-17T08:31:00.000Z",
  "updated": "2017-11-17T08:31:00.000Z",
  "title": "Purity for the Brauer group",
  "authors": [
    "Kestutis Cesnavicius"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "A purity conjecture due to Grothendieck and Auslander--Goldman predicts that the Brauer group of a regular scheme does not change after removing a closed subscheme of codimension $\\ge 2$. The combination of several works of Gabber settles the conjecture except for some cases that concern $p$-torsion Brauer classes in mixed characteristic $(0, p)$. We establish the remaining cases by using the tilting equivalence for perfectoid rings. To reduce to perfectoids, we control the change of the Brauer group of the punctured spectrum of a local ring when passing to a finite flat cover.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-17T08:31:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14F20",
      "14G22",
      "16K50"
    ],
    "keywords": [
      "brauer group",
      "torsion brauer classes",
      "finite flat cover",
      "regular scheme",
      "gabber settles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}