Explicit Rational Equivalences of Zero-cycles on Products of Elliptic Curves

The Chow group of zero-cycles on a surface is a notoriously difficult object to study, but a set of far-reaching conjectures due to Bloch and Beilinson aim to describe the structure of this group. Focusing our attention on products of two elliptic curves, we will specifically consider the subgroup of its Chow group generated by rational points. We will describe a family of surfaces for which the rank of this subgroup is as predicted by Bloch and Beilinson’s conjectures, using rational curves in the Kummer surface to generate rational equivalences.