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We construct an Euler system of generalized Heegner cycles to bound theSelmer group associated to a modular form and an algebraic Hecke character. Themain argument is based on Kolyvagin's machinery explained by Gross while thekey object of the Euler system, the generalized Heegner cycles, were firstconsidered by Bertolini, Darmon and Prasanna.

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