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 (f,χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (,0), with 0<<2r. This generalizes the p-adic Gross-Zagier formula in the case =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 (f,χ), où f est une forme modulaire ordinaire de poids 2r et χ est un caractère de Hecke non-ramifé de type (,0), pour 0<<2r. Ceci généralise la formule de Perrin-Riou (en poids deux) and Nekovář (poids plus élevé).

Received : 2014-08-17
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
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     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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