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# 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.