{
  "id": "2203.16234",
  "version": "v1",
  "published": "2022-03-30T12:09:44.000Z",
  "updated": "2022-03-30T12:09:44.000Z",
  "title": "An analytic viewpoint on the Hasse principle",
  "authors": [
    "Vlerë Mehmeti"
  ],
  "comment": "38 pages, 7 figures; comments welcome",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Working on Berkovich analytic curves, we propose a geometric approach to the study of the Hasse principle over function fields of curves defined over a complete discretely valued field. Using it, we show the Hasse principle to be verified for certain families of projective homogeneous spaces. As a consequence, we also obtain said principle in the already known cases of quadratic forms and homogeneous varieties over unitary groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-30T12:09:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hasse principle",
      "analytic viewpoint",
      "berkovich analytic curves",
      "complete discretely valued field",
      "quadratic forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}