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.