{
  "id": "1706.07019",
  "version": "v1",
  "published": "2017-06-21T17:26:18.000Z",
  "updated": "2017-06-21T17:26:18.000Z",
  "title": "Index of fibrations and Brauer classes that never obstruct the Hasse principle",
  "authors": [
    "Masahiro Nakahara"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth projective variety with a fibration into varieties that either satisfy a condition on representability of zero-cycles or that are torsors under an abelian variety. We study the classes in the Brauer group that never obstruct the Hasse principle for $X$. We prove that if the generic fiber has a zero-cycle of degree $d$ over the generic point, then the Brauer classes whose orders are prime to $d$ do not play a role in the Brauer--Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-21T17:26:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G35",
      "14F22"
    ],
    "keywords": [
      "hasse principle",
      "odd torsion brauer classes",
      "del pezzo surfaces",
      "smooth projective variety",
      "abelian variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}