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September 2019 Kolyvagin systems and Iwasawa theory of generalized Heegner cycles
Matteo Longo, Stefano Vigni
Kyoto J. Math. 59(3): 717-746 (September 2019). DOI: 10.1215/21562261-2019-0005

Abstract

Iwasawa theory of Heegner points on abelian varieties of GL2 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.

Citation

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Matteo Longo. Stefano Vigni. "Kolyvagin systems and Iwasawa theory of generalized Heegner cycles." Kyoto J. Math. 59 (3) 717 - 746, September 2019. https://doi.org/10.1215/21562261-2019-0005

Information

Received: 11 May 2016; Revised: 13 May 2017; Accepted: 18 May 2017; Published: September 2019
First available in Project Euclid: 12 July 2019

zbMATH: 07108009
MathSciNet: MR3990184
Digital Object Identifier: 10.1215/21562261-2019-0005

Subjects:
Primary: 11R23
Secondary: 11F11

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 3 • September 2019
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