On the $p$-adic variation of Heegner points

Abstract

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.

26 pages

References in corpus (1)

• Rankin--Eisenstein classes and explicit reciprocity laws

Cited by in corpus (6)

• The universal $p$-adic Gross-Zagier formula
• P-adic L-functions in universal deformation families
• Interpolation of Generalized Heegner Cycles in Coleman Families
• On the p-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields
• Wide moments of $L$-functions I: Twists by class group characters of imaginary quadratic fields
• Eisenstein degeneration of Euler systems