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.
"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