On the exceptional specializations of big Heegner points
Francesc Castella
TL;DR
This paper extends the p-adic Gross-Zagier formula to a broader setting and derives a new derivative formula for specializations of big Heegner points at exceptional primes within Hida families.
Contribution
It introduces a generalized p-adic Gross-Zagier formula applicable to semistable non-crystalline cases and provides a derivative formula for big Heegner points at exceptional primes.
Findings
Extended the p-adic Gross-Zagier formula to semistable non-crystalline settings.
Derived a new derivative formula for specializations of big Heegner points at exceptional primes.
Connected the formula with Hida families and previous work on Heegner points.
Abstract
We extend the -adic Gross-Zagier formula of Bertolini, Darmon, and Prasanna to the semistable non-crystalline setting, and combine it with our previous work to obtain a derivative formula for the specializations of Howard's big Heegner points at exceptional primes in the Hida family.
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