{
  "id": "2202.07142",
  "version": "v1",
  "published": "2022-02-15T02:26:23.000Z",
  "updated": "2022-02-15T02:26:23.000Z",
  "title": "Brauer-Manin obstruction for Markoff-type cubic surfaces",
  "authors": [
    "Quang-Duc Dao"
  ],
  "comment": "28 pages; all comments and suggestions are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Following the works by Ghosh and Sarnak; Loughran and Mitankin; Colliot-Th\\'el\\`ene, Wei, and Xu, we study the local-global principle and Brauer--Manin obstruction for integral points on similar Markoff-type cubic surfaces. Furthermore, we construct a family of counterexamples to the integral Hasse principle which can be explained by the Brauer--Manin obstruction with a greater frequency, compared to the results given by Loughran and Mitankin; Colliot-Th\\'el\\`ene, Wei, and Xu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-15T02:26:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brauer-manin obstruction",
      "similar markoff-type cubic surfaces",
      "integral hasse principle",
      "greater frequency",
      "integral points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}