Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 3 (2019), 717-746.
Kolyvagin systems and Iwasawa theory of generalized Heegner cycles
Iwasawa theory of Heegner points on abelian varieties of type has been studied by, among others, Mazur, Perrin-Riou, Bertolini, and Howard. The purpose of this article is to describe extensions of some of their results in which abelian varieties are replaced by the Galois cohomology of Deligne’s -adic representation attached to a modular form of even weight greater than . In this setting, the role of Heegner points is played by higher-dimensional Heegner-type cycles that have been recently defined by Bertolini, Darmon, and Prasanna. Our results should be compared with those obtained, via deformation-theoretic techniques, by Fouquet in the context of Hida families of modular forms.
Kyoto J. Math., Volume 59, Number 3 (2019), 717-746.
Received: 11 May 2016
Revised: 13 May 2017
Accepted: 18 May 2017
First available in Project Euclid: 12 July 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11R23: Iwasawa theory
Secondary: 11F11: Holomorphic modular forms of integral weight
Longo, Matteo; Vigni, Stefano. Kolyvagin systems and Iwasawa theory of generalized Heegner cycles. Kyoto J. Math. 59 (2019), no. 3, 717--746. doi:10.1215/21562261-2019-0005. https://projecteuclid.org/euclid.kjm/1562896995