{
  "id": "1807.11517",
  "version": "v1",
  "published": "2018-07-30T18:18:07.000Z",
  "updated": "2018-07-30T18:18:07.000Z",
  "title": "Iwasawa theory for Symmetric Square of non-$p$-ordinary eigenforms",
  "authors": [
    "Kâzım Büyükboduk",
    "Antonio Lei",
    "Guhan Venkat"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Our main goal in this article is to prove a divisibility statement in the Iwasawa main conjectures for symmetric squares of non-$p$-ordinary eigenforms (twisted by an auxiliary Dirichlet character). This task is carried out with the aid of Beilinson-Flach elements, which need to be suitably modified to obtain their integral counterparts. The key technical novelty is a significant improvement of the signed factorization procedure employed in the semi-ordinary Rankin-Selberg products, dwelling on ideas of Perrin-Riou on higher rank Euler systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-30T18:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F11",
      "11R20"
    ],
    "keywords": [
      "symmetric square",
      "ordinary eigenforms",
      "iwasawa theory",
      "higher rank euler systems",
      "auxiliary dirichlet character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}