Interpolation of Generalized Heegner Cycles in Coleman Families
Number Theory
2021-06-18 v2
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 -adic Gross--Zagier formulae at for non-ordinary eigenforms and consequentially, also in the proof of a conjecture of Perrin-Riou.
Keywords
Cite
@article{arxiv.1907.04086,
title = {Interpolation of Generalized Heegner Cycles in Coleman Families},
author = {Kazim Büyükboduk and Antonio Lei},
journal= {arXiv preprint arXiv:1907.04086},
year = {2021}
}
Comments
Several 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