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CATEGORIES:Number Theory Seminar
SUMMARY:The number of conics in a family which contain a r
ational point - Daniel Loughran (Bristol)
DTSTART;TZID=Europe/London:20131203T161500
DTEND;TZID=Europe/London:20131203T171500
UID:TALK47547AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/47547
DESCRIPTION:Given a variety over a number field\, a fundamenta
l problem in number theory is to determine whether
or not it contains a rational point. More general
ly given a family of varieties\, one may ask: "how
many" of these varieties contain a rational point
? The simplest variety one can imagine is a conic\
, but already such problems become non-trivial for
families of conics. Serre proved upper bounds for
some counting functions associated to problems of
this type and asked whether his bounds were sharp
. In this talk we shall address Serre's question f
or some families of conics parametrised by algebra
ic tori.
LOCATION:MR13
CONTACT:James Newton
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