ON THE -ADIC VARIATION OF HEEGNER POINTS

In this paper, we prove an ‘explicit reciprocity law’ relating Howard’s system of big Heegner points to a two-variable $p$-adic $L$-function (constructed here) interpolating the $p$-adic Rankin $L$-series of Bertolini–Darmon–Prasanna 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.

On explicit reciprocity law over formal groups

Let𝔣be a one-dimensional Lubin-Tate formal group overℤp. Colmez (1998) and Perrin-Riou (1994) proved an explicit reciprocity law for tempered distributions over the formal group𝔾m. In this paper, the general explicit reciprocity law over the formal group𝔣is proved.