The Brauer-Manin obstruction for zero-cycles on K3 surfaces

Arithmetic of Rational Points and Zero-cycles on Products of Kummer Varieties and K3 Surfaces

“…FB thanks the Max-Planck-Institut für Mathematik for the financial support and for providing excellent working conditions. The authors are grateful to Alexei Skorobogatov and Damián Gvirtz for useful conversations, to Daniel Loughran for pointing out the recent preprint [Ier18], and to Evis Ieronymou for his interest in this work. They are also indebted to the anonymous referee whose helpful comments improved this paper and its exposition.…”

“…the Max-Planck-Institut für Mathematik for the financial support and for providing excellent working conditions. The authors are grateful to Daniel Loughran for pointing out the recent preprint [Ier18] and thank Evis Ieronymou for his interest in this work.…”

“…After obtaining our results for Kummer varieties, we were made aware of a recent preprint of Ieronymou ([Ier18]) in which he uses Liang's approach together with work of Orr and Skorobogatov in [OS18] to prove analogues of Liang's results in [Lia13] for K3 surfaces. Since Kummer surfaces are both K3 surfaces and Kummer varieties of dimension 2, there is an overlap between our work and that of Ieronymou (note that Ieronymou's results do not require that the degree of the 0-cycle is odd).…”