## Duke Mathematical Journal

### Generalized Heegner cycles and $p$-adic Rankin $L$-series

Massimo Bertolini, Henri Darmon, and Kartik Prasanna

#### 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.

#### Article information

Source
Duke Math. J., Volume 162, Number 6 (2013), 1033-1148.

Dates
First available in Project Euclid: 22 April 2013

https://projecteuclid.org/euclid.dmj/1366639399

Digital Object Identifier
doi:10.1215/00127094-2142056

Mathematical Reviews number (MathSciNet)
MR3053566

Zentralblatt MATH identifier
1302.11043

#### Citation

Bertolini, Massimo; Darmon, Henri; Prasanna, Kartik. Generalized Heegner cycles and $p$ -adic Rankin $L$ -series. Duke Math. J. 162 (2013), no. 6, 1033--1148. doi:10.1215/00127094-2142056. https://projecteuclid.org/euclid.dmj/1366639399

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