{
  "id": "1405.2777",
  "version": "v2",
  "published": "2014-05-12T14:26:49.000Z",
  "updated": "2014-05-19T13:19:11.000Z",
  "title": "Iwasawa theory of Heegner cycles, I. Rank over the Iwasawa algebra",
  "authors": [
    "Matteo Longo",
    "Stefano Vigni"
  ],
  "comment": "Minor modifications; 27 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first in a series of two, is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne's p-adic representation attached to a modular form f of even weight >2. In this more general setting, the role of Heegner points is played by higher-dimensional Heegner cycles in the sense of Nekov\\'a\\v{r}. In particular, we prove that the Pontryagin dual of a certain Bloch-Kato Selmer group associated with f has rank 1 over a suitable anticyclotomic Iwasawa algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-19T13:19:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F11"
    ],
    "keywords": [
      "iwasawa theory",
      "heegner points",
      "abelian varieties",
      "bloch-kato selmer group",
      "higher-dimensional heegner cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2777L"
    }
  }
}