The number of conics in a family which contain a rational point

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• Daniel Loughran (Bristol)
• Tuesday 03 December 2013, 16:15-17:15
• MR13.

If you have a question about this talk, please contact James Newton.

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 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 for some families of conics parametrised by algebraic tori.

This talk is part of the Number Theory Seminar series.

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