We relate the -adic heights of generalized Heegner cycles to the derivative of a -adic -function attached to a pair , where is an ordinary weight newform and is an unramified imaginary quadratic Hecke character of infinity type , with . This generalizes the -adic Gross-Zagier formula in the case due to Perrin-Riou (in weight two) and Nekovář (in higher weight).
Nous relions les hauteurs -adiques des cycles de Heegner généralisés à la dérivée d’une fonction -adique attachée à une paire , où est une forme modulaire ordinaire de poids et est un caractère de Hecke non-ramifé de type , pour . Ceci généralise la formule de Perrin-Riou (en poids deux) and Nekovář (poids plus élevé).
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Keywords: algebraic cycles, modular forms, $p$-adic $L$-functions
Mot clés : cycles algébriques, formes modulaires, fonctions $L$ $p$-adiques
@article{AIF_2016__66_3_1117_0, author = {Shnidman, Ariel}, title = {$p$-adic heights of generalized {Heegner} cycles}, journal = {Annales de l'Institut Fourier}, pages = {1117--1174}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {66}, number = {3}, year = {2016}, doi = {10.5802/aif.3033}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3033/} }
TY - JOUR AU - Shnidman, Ariel TI - $p$-adic heights of generalized Heegner cycles JO - Annales de l'Institut Fourier PY - 2016 SP - 1117 EP - 1174 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3033/ DO - 10.5802/aif.3033 LA - en ID - AIF_2016__66_3_1117_0 ER -
%0 Journal Article %A Shnidman, Ariel %T $p$-adic heights of generalized Heegner cycles %J Annales de l'Institut Fourier %D 2016 %P 1117-1174 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3033/ %R 10.5802/aif.3033 %G en %F 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://archive.numdam.org/articles/10.5802/aif.3033/
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