{
  "id": "1202.4115",
  "version": "v3",
  "published": "2012-02-18T23:09:30.000Z",
  "updated": "2014-06-05T23:51:55.000Z",
  "title": "On the equation N_{K/k}(Ξ)=P(t)",
  "authors": [
    "Dasheng Wei"
  ],
  "comment": "34 pages, Theorem 3.5 is generalized to any prime p (not only p=3). Proc. London Math. Soc. (to appear)",
  "categories": [
    "math.NT"
  ],
  "abstract": "For varieties given by an equation N_{K/k}(\\Xi)=P(t), where N_{K/k} is the norm form attached to a field extension K/k and P(t) in k[t] is a polynomial, three topics have been investigated: (1) computation of the unramified Brauer group of such varieties over arbitrary fields; (2) rational points and Brauer-Manin obstruction over number fields (under Schinzel's hypothesis); (3) zero-cycles and Brauer-Manin obstruction over number fields. In this paper, we produce new results in each of three directions. We obtain quite general results under the assumption that K/k is abelian (as opposed to cyclic in earlier investigation).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-05T23:51:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14G05"
    ],
    "keywords": [
      "brauer-manin obstruction",
      "number fields",
      "field extension k/k",
      "quite general results",
      "unramified brauer group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4115W"
    }
  }
}