Duke Mathematical Journal

Generalized Heegner cycles and p-adic Rankin L-series

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
Appendix by Brian Conrad

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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

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

First available in Project Euclid: 22 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
Secondary: 11G35: Varieties over global fields [See also 14G25] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 11G05: Elliptic curves over global fields [See also 14H52]


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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