Kyoto Journal of Mathematics

Kolyvagin systems and Iwasawa theory of generalized Heegner cycles

Abstract

Iwasawa theory of Heegner points on abelian varieties of $\operatorname{GL}_{2}$ 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 $p$-adic representation attached to a modular form of even weight greater than $2$. 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.

Article information

Source
Kyoto J. Math., Volume 59, Number 3 (2019), 717-746.

Dates
Revised: 13 May 2017
Accepted: 18 May 2017
First available in Project Euclid: 12 July 2019

https://projecteuclid.org/euclid.kjm/1562896995

Digital Object Identifier
doi:10.1215/21562261-2019-0005

Mathematical Reviews number (MathSciNet)
MR3990184

Zentralblatt MATH identifier
07108009

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11F11: Holomorphic modular forms of integral weight

Citation

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

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