# Rational Equivalences on Products of Elliptic Curves in a Family

@article{Love2020RationalEO,
title={Rational Equivalences on Products of Elliptic Curves in a Family},
author={Jonathan Love},
journal={arXiv: Algebraic Geometry},
year={2020}
}
Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson predicts that the image of this map is finite when $k$ is a number field. We construct a $2$-parameter family of elliptic curves that can be used to produce examples of pairs $E_1,E_2$ where this image is finite. The family is constructed to guarantee the existence of a rational curve passing through a… Expand

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