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SUMMARY:Arithmetic of zero-cycles on products of Kummer varieties and K3 s
 urfaces
DTSTART:20181114T140000
DTEND:20181114T150000
DTSTAMP:20260427T224135Z
UID:28efe005ad89ac92ffcd2e0cdcbc3a89b44a06d699544aa4cd0171d2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Francesca Balestrieri (Max Planck Institute\, Bonn)\nThe follo
 wing is joint work with Rachel Newton. In the spirit of work by Yongqi Lia
 ng\, we relate the arithmetic of rational points to that of zero-cycles fo
 r the class of Kummer varieties over number fields. In particular\, if X i
 s any Kummer variety over a number field k\, we show that if the Brauer-Ma
 nin obstruction is the only obstruction to the existence of rational point
 s 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 degre
 e on X. Building on this result and on some other recent results by Ierony
 mou\, Skorobogatov and Zarhin\, we further prove a similar Liang-type resu
 lt for products of Kummer varieties and K3 surfaces over k.
LOCATION:MA A1 12 https://plan.epfl.ch/?room=MAA112
STATUS:CONFIRMED
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