On the exceptional specializations of big heegner points

We extend the -adic Gross-Zagier formula of Bertolini et al. [Generalized Heegner cycles and -adic Rankin -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.