Heights of Generalized Heegner Cycles.

Abstract

We relate the derivative of a p-adic Rankin-Selberg L-function to p-adic heights of the generalized Heegner cycles introduced by Bertolini, Darmon, and Prasanna. This generalizes the p-adic Gross-Zagier formulas of Perrin-Riou and Nekovar by allowing for Hecke characters of infinite order. As an application, we prove special cases of Perrin-Riou's p-adic Bloch-Kato conjecture. We also construct a Green's kernel in order to compute archimedean heights of generalized Heegner cycles. These computations will eventually lead to an archimedean version of our formula, generalizing the higher weight Gross-Zagier formula due to Zhang.