On the Selmer group attached to a modular form and an algebraic Hecke character

We construct an Euler system of generalized Heegner cycles to bound the Selmer group associated to a modular form and an algebraic Hecke character. The main argument is based on Kolyvagin’s method adapted by Bertolini and Darmon (J Reine Angew Math 412:63–74, 1990 ) and by Nekovář (Invent Math 107(1):99–125, 1992 ), while the key object of the Euler system, the generalized Heegner cycles were first considered by Bertolini et al. (Duke Math J 162(6):1033–1148, 2013 ).