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SUMMARY:The number of conics in a family which contain a rational point - 
 Daniel Loughran (Bristol)
DTSTART:20131203T161500Z
DTEND:20131203T171500Z
UID:TALK47547@talks.cam.ac.uk
CONTACT:James Newton
DESCRIPTION:Given a variety over a number field\, a fundamental problem in
  number theory is to determine whether or not it contains a rational point
 . More generally given a family of varieties\, one may ask: "how many" of 
 these varieties contain a rational point? The simplest variety one can ima
 gine is a conic\, but already such problems become non-trivial for familie
 s of conics. Serre proved upper bounds for some counting functions associa
 ted to problems of this type and asked whether his bounds were sharp. In t
 his talk we shall address Serre's question for some families of conics par
 ametrised by algebraic tori.
LOCATION:MR13
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