{
  "id": "2302.01640",
  "version": "v1",
  "published": "2023-02-03T10:30:14.000Z",
  "updated": "2023-02-03T10:30:14.000Z",
  "title": "The Cassels-Tate pairing on 2-Selmer groups of elliptic curves",
  "authors": [
    "Himanshu Shukla",
    "Michael Stoll"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This leads to a new proof that a pairing defined by Cassels on the 2-Selmer groups of elliptic curves agrees with the Cassels-Tate pairing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-03T10:30:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11Y99"
    ],
    "keywords": [
      "elliptic curve",
      "cassels-tate pairing",
      "albanese-albanese definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}