In the first part of the talk\, I will introduce some of the str ategies used when studying the arithmetic of rational points and zero-cycl es on varieties over number fields. In particular\, I will talk about loca l-global principles and obstruction sets (e.g. the Brauer-Manin set)\, and I will explain how one could use the theory of obstruction sets to classi fy varieties according to the arithmetic behaviour of their rational point s and zero-cycles.In the second part of the talk\, I will present the foll owing joint work with Rachel Newton. In the spirit of some results by Yong qi Liang\, we relate the arithmetic of rational points to that of zero-cyc les for the class of Kummer varieties. In particular\, if X is any Kummer variety over a number field k\, we show that if the BrauerManin obstructio n is the only obstruction to the existence of rational points on X over al l finite extensions of k\, then the BrauerManin obstruction is the only ob struction to the existence of a zero-cycle of any odd degree on X. Buildin g on this result and on some other recent results by Ieronymou\, Skoroboga tov and Zarhin\, we further prove a similar Liang-type result for products of Kummer varieties and K3 surfaces over k.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:swheatle@ist.ac.at SUMMARY:Arithmetic of zero-cycles on products of Kummer varieties and K3 su rfaces URL:https://talks-calendar.app.ist.ac.at/events/1397 END:VEVENT END:VCALENDAR