{
  "id": "1907.08810",
  "version": "v1",
  "published": "2019-07-20T13:35:25.000Z",
  "updated": "2019-07-20T13:35:25.000Z",
  "title": "Vanishing of the Brauer group of a del Pezzo surface of degree 4",
  "authors": [
    "Manar Riman"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We explicitly construct a del Pezzo surface $X$ of degree 4 over a field $k$ such that $\\operatorname{H}^1(k,\\operatorname{Pic}\\overline X)$ is isomorphic to $\\mathbb{ZZ}/2\\mathbb{Z}$ while $\\operatorname{Br} X/\\operatorname{Br} k$ is trivial. This proves that the algorithm to compute the Brauer group in [VAV] cannot be generalized in some cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-20T13:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14G05"
    ],
    "keywords": [
      "del pezzo surface",
      "brauer group",
      "explicitly construct",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}