The $p$-adic Gross-Zagier formula on Shimura curves, II: nonsplit primes

Abstract

The formula of the title relates $p$-adic heights of Heegner points and derivatives of $p$-adic $L$-functions. It was originally proved by Perrin-Riou for $p$-ordinary elliptic curves over the rationals, under the assumption that $p$ splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.

38 pages, 1 figure. Appendix B contains a list of errata to arXiv:1510.02114. New in this version: a correction as Appendix C, to appear separately in JIMJ

References in corpus (3)

• The universal $p$-adic Gross-Zagier formula
• $p$-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou
• p-adic equidistribution of CM points

Cited by in corpus (3)

• The universal $p$-adic Gross-Zagier formula
• p-adic equidistribution of CM points
• $p$-adic L-functions via local-global interpolation: the case of ${\mathrm{GL}}_2\times \mathrm{GU}(1)$