{
  "id": "1008.0596",
  "version": "v1",
  "published": "2010-08-03T17:23:53.000Z",
  "updated": "2010-08-03T17:23:53.000Z",
  "title": "Failure of the Hasse principle for Enriques surfaces",
  "authors": [
    "Anthony Várilly-Alvarado",
    "Bianca Viray"
  ],
  "comment": "16 pages, 2 tables, Magma code included at the end of the source file",
  "journal": "Adv. Math. 226 (2011), 4884-4901",
  "doi": "10.1016/j.aim.2010.12.020",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We construct an Enriques surface X over Q with empty \\'etale-Brauer set (and hence no rational points) for which there is no algebraic Brauer-Manin obstruction to the Hasse principle. In addition, if there is a transcendental obstruction on X, then we obtain a K3 surface that has a transcendental obstruction to the Hasse principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-03T17:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14G05",
      "14G25",
      "14G40"
    ],
    "keywords": [
      "hasse principle",
      "enriques surface",
      "transcendental obstruction",
      "empty etale-brauer set",
      "algebraic brauer-manin obstruction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0596V"
    }
  }
}