Heights of Generalized Heegner Cycles.

[摘要] We relate the derivative of a p-adic Rankin-Selberg L-function to p-adic heights of the generalized Heegner cycles introduced by Bertolini, Darmon, and Prasanna.This generalizes the p-adic Gross-Zagier formulas of Perrin-Riou and Nekovar by allowing for Hecke characters of infinite order.As an application, we prove special cases of Perrin-Riou;;s p-adic Bloch-Kato conjecture.We also construct a Green;;s kernel in order to compute archimedean heights of generalized Heegner cycles.These computations will eventually lead to an archimedean version of our formula, generalizing the higher weight Gross-Zagier formula due to Zhang.

[发布机构] University of Michigan

[效力级别] L-functions

[关键词] algebraic cycles;L-functions;arithmetic geometry;number theory;Mathematics;Science;Mathematics