We extend the
-adic Gross–Zagier formula of Bertolini et al. [Generalized Heegner cycles and
-series, Duke Math. J.
162(6) (2013), 1033–1148] to the semistable non-crystalline setting, and combine it with our previous work [Castella, On the
-adic variation of Heegner points, Preprint, 2014, arXiv:1410.6591] to obtain a derivative formula for the specializations of Howard’s big Heegner points [Howard, Variation of Heegner points in Hida families, Invent. Math.
167(1) (2007), 91–128] at exceptional primes in the Hida family.