{
  "id": "2106.14511",
  "version": "v1",
  "published": "2021-06-28T09:54:36.000Z",
  "updated": "2021-06-28T09:54:36.000Z",
  "title": "On the Bloch--Kato conjecture for GSp(4) x GL(2)",
  "authors": [
    "David Loeffler",
    "Sarah Livia Zerbes"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the Bloch--Kato conjecture for certain critical values of degree 8 $L$-functions associated to cusp forms on $\\mathrm{GSp}_4 \\times \\mathrm{GL}_2$. We also construct a $p$-adic Eichler--Shimura isomorphism in Hida families for $\\mathrm{GSp}_4$, relating $H^2$ of automorphic vector bundles with $\\mathbf{D}_{\\mathrm{cris}}$ of a subquotient of \\'etale cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-28T09:54:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11F67",
      "11F80",
      "11R23"
    ],
    "keywords": [
      "bloch-kato conjecture",
      "adic eichler-shimura isomorphism",
      "automorphic vector bundles",
      "cusp forms",
      "hida families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}