Heegner cycles and higher weight specializations of big Heegner points

Let be a -ordinary Hida family of tame level , and let be an imaginary quadratic field satisfying the Heegner hypothesis relative to . By taking a compatible sequence of twisted Kummer images of CM points over the tower of modular curves of level , Howard has constructed a canonical class in the cohomology of a self-dual twist of the big Galois representation associated to . If a -ordinary eigenform on of weight is the specialization of at , one thus obtains from a higher weight generalization of the Kummer images of Heegner points. In this paper we relate the classes to the ,tale Abel-Jacobi images of Heegner cycles when splits in .