Number Theory seminar

Number Theory Seminar

Daniel Loughran (Hannover)

Title: Fibrations with few rational points

Abstract: In this talk, we study the problem of counting the number of varieties in fibrations over projective spaces which contain a rational point. We obtain geometric conditions that force very few of the varieties in the family to contain a rational point, in a precise quantitative sense. This generalises the special case of conic bundles treated by Serre.

This is joint work with Arne Smeets.