$p$-adic heights of generalized Heegner cycles
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1117-1174

We relate the $p$-adic heights of generalized Heegner cycles to the derivative of a $p$-adic $L$-function attached to a pair $\left(f,\chi \right)$, where $f$ is an ordinary weight $2r$ newform and $\chi$ is an unramified imaginary quadratic Hecke character of infinity type $\left(\ell ,0\right)$, with $0<\ell <2r$. This generalizes the $p$-adic Gross-Zagier formula in the case $\ell =0$ due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

Nous relions les hauteurs $p$-adiques des cycles de Heegner généralisés à la dérivée d’une fonction $L$ $p$-adique attachée à une paire $\left(f,\chi \right)$, où $f$ est une forme modulaire ordinaire de poids $2r$ et $\chi$ est un caractère de Hecke non-ramifé de type $\left(\ell ,0\right)$, pour $0<\ell <2r$. Ceci généralise la formule de Perrin-Riou (en poids deux) and Nekovář (poids plus élevé).

Revised : 2015-02-09
Accepted : 2015-06-11
Published online : 2016-12-14
DOI : https://doi.org/10.5802/aif.3033
Classification:  11G40,  11G18
Keywords: algebraic cycles, modular forms, $p$-adic $L$-functions
@article{AIF_2016__66_3_1117_0,
author = {Shnidman, Ariel},
title = {$p$-adic heights of generalized Heegner cycles},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {66},
number = {3},
year = {2016},
pages = {1117-1174},
doi = {10.5802/aif.3033},
language = {en},
url = {http://www.numdam.org/item/AIF_2016__66_3_1117_0}
}

Shnidman, Ariel. $p$-adic heights of generalized Heegner cycles. Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 1117-1174. doi : 10.5802/aif.3033. http://www.numdam.org/item/AIF_2016__66_3_1117_0/

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