$p$-adic heights of generalized Heegner cycles

Abstract

We relate the $p$-adic heights of generalized Heegner cycles to the derivative of a $p$-adic $L$-function attached to a pair $(f,\chi )$, where $f$ is an ordinary weight $2r$ newform and $\chi$ is an unramified imaginary quadratic Hecke character of infinity type $(\ell ,0)$, 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 Nekováur (in higher weight).

42 pages, added details and clarity to Sections 1, 7, and 8

References in corpus (2)

• On the Selmer group attached to a modular form and an algebraic Hecke character
• Heegner cycles and $p$-adic $L$-functions