{
  "id": "2011.14524",
  "version": "v1",
  "published": "2020-11-30T03:33:47.000Z",
  "updated": "2020-11-30T03:33:47.000Z",
  "title": "Weil-Chatelet Groups of Rational Elliptic Surfaces",
  "authors": [
    "Nadir Hajouji"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We classify pairs $(S, \\gamma)$, consisting of a rational elliptic surface $S$ and a Galois cover $\\gamma$ of the base, which satisfy a condition we call $\\mathcal{L}$-stability. We explain how to use the theory of Mordell-Weil lattices to compute the kernel of the restriction maps of Weil-Chatelet groups for $\\mathcal{L}$-stable pairs. We also prove results about the injectivity of restriction maps of Weil-Chatelet groups for some pairs which are not $\\mathcal{L}$-stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-30T03:33:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational elliptic surface",
      "weil-chatelet groups",
      "restriction maps",
      "galois cover",
      "mordell-weil lattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}