Interpolation of Generalized Heegner Cycles in Coleman Families

Abstract

Kobayashi recently proved that the generalized Heegner cycles of Bertolini--Darmon--Prasanna can be interpolated along the anticyclotomic tower, giving rise to distribution valued cohomology classes with expected growth rate. We interpolate these classes along Coleman families. This construction plays a role in the proofs of $p$-adic Gross--Zagier formulae at for non-ordinary eigenforms and consequentially, also in the proof of a conjecture of Perrin-Riou.