Generalized Heegner cycles and p-adic Rankin L-series

Abstract

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.