{
  "id": "2112.00843",
  "version": "v2",
  "published": "2021-12-01T21:42:33.000Z",
  "updated": "2022-02-08T09:43:01.000Z",
  "title": "Ramified descent",
  "authors": [
    "Julian Lawrence Demeio"
  ],
  "comment": "30 pages. Comments welcomed!",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We investigate the \"ramified descent problem\": which adelic points of a smooth geometrically connected variety $X$ defined over a number field $K$ can be approximated by points that lift to a (twist of a) given ramified cover? We show that the natural descent set corresponding to the problem defines an obstruction to Hasse Principle and weak approximation. Furthermore, we introduce a Brauer-Manin obstruction to the problem. This obstruction can be purely transcendental (and non-trivial) even for abelian covers, which answers in the negative a question posed by Harari at a 2019 workshop. Moreover, the counterexample we produce is also an explicit example of transcendental obstruction to weak approximation for a quotient $SL_n/G$, with $G$ constant metabelian.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-08T09:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "14G12",
      "11G35"
    ],
    "keywords": [
      "weak approximation",
      "smooth geometrically connected variety",
      "number field",
      "natural descent set corresponding",
      "ramified descent problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}