BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Number Theory Seminar
SUMMARY:Arithmetic of rational points and zero-cycles on K
ummer varieties - Rachel Newton (University of Rea
ding)
DTSTART;TZID=Europe/London:20180501T143000
DTEND;TZID=Europe/London:20180501T153000
UID:TALK105409AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/105409
DESCRIPTION:In 1970\, Manin observed that the Brauer group Br(
X) of a variety X over a number field K can obstru
ct the Hasse principle on X. In other words\, the
lack of a K-point on X despite the existence of po
ints over every completion of K is sometimes expla
ined by non-trivial elements in Br(X). This so-cal
led Brauer-Manin obstruction may not always suffic
e to explain the failure of the Hasse principle bu
t it is known to be sufficient for some classes of
varieties (e.g. torsors under connected algebraic
groups) and conjectured to be sufficient for rati
onally connected varieties and K3 surfaces.\nA zer
o-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 easier to study the zero
-cycles of degree 1 on X\, rather than the rationa
l points. Yongqi Liang has shown that for rational
ly connected varieties\, sufficiency of the Brauer
-Manin obstruction to the existence of rational po
ints over all finite extensions of K implies suffi
ciency of the Brauer-Manin obstruction to the exis
tence of zero-cycles of degree 1 over K. I will di
scuss joint work with Francesca Balestrieri where
we extend Liang's result to Kummer varieties.
LOCATION:MR13
CONTACT:Jack Thorne
END:VEVENT
END:VCALENDAR