Heights of Generalized Heegner Cycles.

algebraic cycles;L-functions;arithmetic geometry;number theory;Mathematics;Science;Mathematics

Shnidman, ArielSnowden, Andrew ;

University of Michigan

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

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113442/shnidman_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.