Generalized Heegner cycles and p-adic Rankin L-series

This article studies a distinguished collection of so-called generalized Heegner cycles in the product of a Kuga-Sato variety with a power of a CM elliptic curve. Its main result is a p-adic analogue of the Gross-Zagier formula which relates the images of generalized Heegner cycles under the p-adic Abel-Jacobi map to the special values of certain p-adic Rankin L-series at critical points that lie outside their range of classical interpolation.