On the non-triviality of the p-adic Abel-Jacobi image of generalised Heegner cycles modulo p, I: modular curves

2014/10/01 by Burungale, Ashay A.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1410.0300

Abstract

Generalised Heegner cycles are associated to a pair of an elliptic Hecke eigenform and a Hecke character over an imaginary quadratic extension K/\Q. Let p be an odd prime split in K/\Q and l≠ p an odd unramified prime. We prove the non-triviality of the p-adic Abel-Jacobi image of generalised Heegner cycles modulo p over the \Z_l-anticylotomic extension of K. The result is an evidence for the refined Bloch-Beilinson and the Bloch-Kato conjecture. In the case of two, it provides a refinement of the results of Cornut and Vatsal on the non-triviality of Heegner points over the \Z_l-anticylotomic extension of K.

Related

• Generalized Heegner cycles and p-adic L-functions in a quaternionic setting
• p-adic Higher Green's Functions for Stark-Heegner Cycles
• A refined Beilinson-Bloch conjecture for motives of modular forms
• Generalized Heegner cycles on Mumford curves
• On the structure of the Bloch--Kato Selmer groups of modular forms over anticyclotomic Z_p-towers