Abstract

In this thesis, we generalize the p-adic Gross-Zagier formula of Darmon-Rotger on triple
product p-adic L-functions to finite slope families. First, we recall the construction of triple product
p-adic L-functions for finite slope families developed by Andreatta-Iovita. Then we proceed to
compute explicitly the p-adic Abel-Jacobi image of the generalized diagonal cycle. We also
establish a theory of finite polynomial cohomology with coefficients for varieties with good
reduction. It simplifies the computation of the p-adic Abel-Jacobi map and has the potential to be
applied to more general settings. Finally, we show by q-expansion principle that the special value
of the L-function is equal to the Abel-Jacobi image. Hence, we conclude the formula.