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

Ashay A. Burungale

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arXiv · 1410.0300

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

Ashay A. Burungale

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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 $l\neq p$ 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 $K$.

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BibTeX RIS

Ashay A. Burungale. 2014-10-01. On the non-triviality of the $p$-adic Abel-Jacobi image of generalised Heegner cycles modulo $p$, I: modular curves. https://arxiv.org/abs/1410.0300

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