Joint PU/IAS Number Theory

When an algebraic variety over the rational numbers contains infinitely many rational points, we may study their distribution. In particular, for Fano varieties, the asymptotic behavior of the number of rational points of bounded height is predicted by Manin’s conjecture.

In this talk, we discuss a proof of Manin’s conjecture for smooth spherical Fano threefolds. In one case, in order to obtain the expected asymptotic formula, it is necessary to exclude a thin subset with exceptionally many rational points from the count. This is joint work with V. Blomer, J. Brüdern and G. Gagliardi.