Francesc Castella

P-adic L-functions and Euler systems: A tale in two trilogies

© Cambridge University Press 2014. This chapter surveys six different special value formulae for p-adic L-functions, stressing their common features and their eventual arithmetic applications via Kolyvagin’s theory of “Euler systems”, in the spirit of Coates-Wiles and Kato-Perrin-Riou.

On the exceptional specializations of big Heegner points

We extend the

Heegner cycles and higher weight specializations of big Heegner points

p

Heegner cycles and p -adic L -functions

-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 Howards big Heegner points at exceptional primes in the Hida family.