# Integral points of bounded height on toric varieties — reloaded

## Antoine Chambert-Loir

We study the analogue for integral points of
the Manin-Peyre conjecture about the number and distribution
of rational points of bounded height. In view of the successes
of the Fourier-theoretic method in the years
1995-2000, the case of equivariant (partial) compactifications of
algebraic groups is particularly promising. Ten years ago, after Yuri
Tschinkel and I had treated the case of vector groups,
we released a preprint that claims to tackle the case of tori.
Unfortunately, the proof there
is incomplete, and a counterexample of Florian Wilsch demonstrates
that the situation is more complicated.
The goal of the lecture is to present the Fourier-theoretic method,
the kind of output it leads to, and to present the new obstruction
that arises, with the hope that it will suffice to describe the
asymptotic number and distribution of integral points of bounded
height on toric varieties.