In this paper, we prove an 'explicit reciprocity law' relating Howard's system of big Heegner points to a two-variable-Adic-function (constructed here) interpolating the-Adic Rankin-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.
|Number of pages
|Journal of the Institute of Mathematics of Jussieu
|Published - Nov 1 2020
All Science Journal Classification (ASJC) codes
- General Mathematics
- 2010 Mathematics subject classification: 11G05 11G40