{
  "id": "1307.7641",
  "version": "v2",
  "published": "2013-07-29T16:54:03.000Z",
  "updated": "2015-01-28T18:22:01.000Z",
  "title": "Norm forms for arbitrary number fields as products of linear polynomials",
  "authors": [
    "Tim Browning",
    "Lilian Matthiesen"
  ],
  "comment": "71 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. We show that any smooth model of the affine variety defined by the equation N_{K/Q} (k) = P(t) satisfies the Hasse principle and weak approximation whenever the Brauer-Manin obstruction is empty. Our proof is based on a combination of methods from additive combinatorics due to Green-Tao and Green-Tao-Ziegler, together with an application of the descent theory of Colliot-Th\\'el\\`ene and Sansuc.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-29T16:54:03.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-28T18:22:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary number fields",
      "norm forms",
      "linear polynomials",
      "field extension",
      "brauer-manin obstruction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 71,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7641B"
    }
  }
}