ON THE EXCEPTIONAL SPECIALIZATIONS OF BIG HEEGNER POINTS

Abstract

We extend the$p$-adic Gross–Zagier formula of Bertoliniet al.[Generalized Heegner cycles and$p$-adic Rankin$L$-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$p$-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.