{
  "id": "1703.02187",
  "version": "v1",
  "published": "2017-03-07T02:49:55.000Z",
  "updated": "2017-03-07T02:49:55.000Z",
  "title": "Degree and the Brauer-Manin obstruction",
  "authors": [
    "Brendan Creutz",
    "Bianca Viray"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let X be a smooth variety over a number field k embedded as a degree d subvariety of $\\mathbb{P}^n$ and suppose that X is a counterexample to the Hasse principle explained by the Brauer-Manin obstruction. We consider the question of whether the obstruction is given by the d-primary subgroup of the Brauer group, which would have both theoretic and algorithmic implications. We prove that this question has a positive answer in the case of torsors under abelian varieties, Kummer varieties and (conditional on finiteness of Tate-Shafarevich groups) bielliptic surfaces. In the case of Kummer varieties we show, more specifically, that the obstruction is already given by the 2-primary torsion. We construct a conic bundle over an elliptic curve that shows that, in general, the answer is no.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T02:49:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G35",
      "14F22"
    ],
    "keywords": [
      "brauer-manin obstruction",
      "kummer varieties",
      "algorithmic implications",
      "conic bundle",
      "number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}