{
  "id": "2106.05322",
  "version": "v1",
  "published": "2021-06-09T18:27:13.000Z",
  "updated": "2021-06-09T18:27:13.000Z",
  "title": "Iwasawa theory for ${\\rm GL}_2\\times{\\rm GL}_2$ and diagonal cycles",
  "authors": [
    "Raúl Alonso",
    "Francesc Castella",
    "Óscar Rivero"
  ],
  "comment": "46 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct an anticyclotomic Euler system for the Rankin--Selberg convolution of two modular forms, using $p$-adic families of generalized Gross--Kudla--Schoen diagonal cycles. As applications of this construction, we prove new cases of the Bloch--Kato conjecture in analytic rank zero (and results towards new cases in analytic rank one), and a divisibility towards an Iwasawa main conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-09T18:27:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F85",
      "14G35"
    ],
    "keywords": [
      "iwasawa theory",
      "analytic rank zero",
      "iwasawa main conjecture",
      "generalized gross-kudla-schoen diagonal cycles",
      "anticyclotomic euler system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}