On the cycle map for products of elliptic curves over a $p$-adic field

TL;DR

This paper investigates the structure of the Chow group of zero-cycles on the product of elliptic curves over a p-adic field, focusing on the image of the Albanese kernel via the cycle class map.

Contribution

It provides new insights into the cycle map structure for products of elliptic curves over p-adic fields, a topic with limited prior understanding.

Findings

Determines the structure of the image of the Albanese kernel

Analyzes the cycle class map for these abelian varieties

Contributes to understanding zero-cycle groups over p-adic fields

Abstract

We study the Chow group of $0$-cycles on the product of elliptic curves over a $p$-adic field. For this abelian variety, it is decided that the structure of the image of the Albanese kernel by the cycle class map.