{
  "id": "1804.10993",
  "version": "v1",
  "published": "2018-04-29T21:21:53.000Z",
  "updated": "2018-04-29T21:21:53.000Z",
  "title": "On the Iwasawa main conjectures for modular forms at non-ordinary primes",
  "authors": [
    "Francesc Castella",
    "Mirela Çiperiani",
    "Christopher Skinner",
    "Florian Sprung"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on the study of the two-variable analogues of these conjectures formulated by B\\\"uy\\\"ukboduk--Lei for imaginary quadratic fields in which $p$ splits, and on anticyclotomic Iwasawa theory. As application of our results, we deduce the $p$-part of the Birch and Swinnerton-Dyer formula in analytic ranks $0$ or $1$ for abelian varieties over $\\mathbb{Q}$ of ${\\rm GL}_2$-type for non-ordinary primes $p>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-29T21:21:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iwasawa main conjectures",
      "non-ordinary primes",
      "modular forms",
      "anticyclotomic iwasawa theory",
      "imaginary quadratic fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}