Abstract
In this paper, we prove an âexplicit reciprocity lawâ relating Howardâs system of big Heegner points to a two-variable$p$-adic$L$-function (constructed here) interpolating the$p$-adic Rankin$L$-series of BertoliniâDarmonâPrasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.
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