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SUMMARY:Arithmetic of rational points and zero-cycles on Kummer varieties 
 - Rachel Newton (University of Reading)
DTSTART:20180501T133000Z
DTEND:20180501T143000Z
UID:TALK105409@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:In 1970\, Manin observed that the Brauer group Br(X) of a vari
 ety X over a number field K can obstruct the Hasse principle on X. In othe
 r words\, the lack of a K-point on X despite the existence of points over 
 every completion of K is sometimes explained by non-trivial elements in Br
 (X). This so-called Brauer-Manin obstruction may not always suffice to exp
 lain the failure of the Hasse principle but it is known to be sufficient f
 or some classes of varieties (e.g. torsors under connected algebraic group
 s) and conjectured to be sufficient for rationally connected varieties and
  K3 surfaces.\nA zero-cycle on X is a formal sum of closed points of X. A 
 rational point of X over K is a zero-cycle of degree 1. It is sometimes ea
 sier to study the zero-cycles of degree 1 on X\, rather than the rational 
 points. Yongqi Liang has shown that for rationally connected varieties\, s
 ufficiency of the Brauer-Manin obstruction to the existence of rational po
 ints over all finite extensions of K implies sufficiency of the Brauer-Man
 in obstruction to the existence of zero-cycles of degree 1 over K. I will 
 discuss joint work with Francesca Balestrieri where we extend Liang's resu
 lt to Kummer varieties.
LOCATION:MR13
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