Karl Van Valckenborgh, Université de Louvain

Rational points on orbifolds

In this talk, I will describe how to determine an asymptotic
formula for the set of rational points of bounded height
(a₀:...:a_n-1) ∈ P^n-1(Q) (using the classical height function)
such that a_i is a squareful integer and Σ_{0 ≤ i ≤ n-1} a_i is also
squareful. The main tool I used to obtain this result is the
Hardy-Littlewood circle method. I will also explain how this
problem fits into the arithmetic Campana program and how
it might be connected with the Manin conjecture.