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

Balestrieri, F. and Newton, R. ORCID: https://orcid.org/0000-0003-4925-635X (2019) Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces. International Mathematics Research Notices. pp. 1-25. ISSN 1073-7928 doi: 10.1093/imrn/rny303

Abstract/Summary

Let k be a number field. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of k to that of zero-cycles over k for Kummer varieties over k. For example, for any Kummer variety X over k, we show that if the Brauer-Manin obstruction is the only obstruction to the Hasse principle for rational points on X over all finite extensions of k, then the (2-primary) Brauer-Manin obstruction is the only obstruction to the Hasse principle for zero-cycles of any given odd degree on X over k. We also obtain similar results for products of Kummer varieties, K3 surfaces and rationally connected varieties.