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DTSTART:20180325T030000
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DTSTART:20181028T020000
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DTSTAMP:20210726T175135Z
UID:5b962b402cbf9667644318@ist.ac.at
DTSTART:20180918T130000
DTEND:20180918T150000
DESCRIPTION:Speaker: Francesca Balestrieri\nhosted by Timothy Browning\nAbs
tract: In the first part of the talk\, I will introduce some of the strate
gies used when studying the arithmetic of rational points and zero-cycles
on varieties over number fields. In particular\, I will talk about local-g
lobal principles and obstruction sets (e.g. the Brauer-Manin set)\, and I
will explain how one could use the theory of obstruction sets to classify
varieties according to the arithmetic behaviour of their rational points a
nd zero-cycles.In the second part of the talk\, I will present the followi
ng joint work with Rachel Newton. In the spirit of some results by Yongqi
Liang\, we relate the arithmetic of rational points to that of zero-cycles
for the class of Kummer varieties. In particular\, if X is any Kummer var
iety over a number field k\, we show that if the BrauerManin obstruction i
s the only obstruction to the existence of rational points on X over all f
inite extensions of k\, then the BrauerManin obstruction is the only obstr
uction to the existence of a zero-cycle of any odd degree on X. Building o
n this result and on some other recent results by Ieronymou\, Skorobogatov
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
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