p-adic heights of generalized Heegner cycles
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, pp. 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:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3033
Classification: 11G40,  11G18
Keywords: algebraic cycles, modular forms, p-adic L-functions
Shnidman, Ariel 1

1 Department of Mathematics Boston College, Chestnut Hill MA 02467 (U.S.A.)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3033/

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