# Arithmetic of zero-cycles on products of Kummer varieties and K3 surfaces

## Francesca Balestrieri

The following is joint work with Rachel Newton. In the spirit of work by Yongqi Liang, we relate the arithmetic of rational points to that of zero-cycles for the class of Kummer varieties over number fields. In particular, if \(X\) is any Kummer variety over a number field \(k\), we show that if the Brauer-Manin obstruction is the only obstruction to the existence of rational points on \(X\) over all finite extensions of \(k\), then the Brauer-Manin obstruction is the only obstruction to the existence of a zero-cycle of any odd degree on \(X\). Building on this result and on some other recent results by Ieronymou, Skorobogatov and Zarhin, we further prove a similar Liang-type result for products of Kummer varieties and K3 surfaces over k.