{
  "id": "2104.03431",
  "version": "v1",
  "published": "2021-04-07T23:38:00.000Z",
  "updated": "2021-04-07T23:38:00.000Z",
  "title": "Recent developments of the Uniform Mordell-Lang Conjecture",
  "authors": [
    "Ziyang Gao"
  ],
  "comment": "This survey focuses on presenting the results (different types and grades), presenting the key new ingredients and explain in details how these new ingredients are applied. Comments are welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture is proved by combining Dimitrov-Gao-Habegger (https://annals.math.princeton.edu/articles/17715) and K\\\"{u}hne (arXiv:2101.10272). We include in this survey a detailed proof on how to combine these two results, which was implicitly done in another short paper of Dimitrov-Gao-Habegger (arXiv:2009.08505) but not explicitly written in existing literature. At the end of the survey we state some future aspects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T23:38:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G50",
      "14G25",
      "14K15"
    ],
    "keywords": [
      "uniform mordell-lang conjecture",
      "developments",
      "online talk",
      "expository survey",
      "full version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}