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.

arXiv commentSeveral sections have been expanded and rewritten. We have added Appendix B, which discusses the interpolation of generalized Heegner cycles over wide-open discs and will serve as an addendum to the published version of the article

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• The universal $p$-adic Gross-Zagier formula
• Heegner points in Coleman families