Diophantine approximation and local distribution of rational points

rational points
Diophantine approximation
grenoble
[MATH]Mathematics [math]
Arakelov Geometry and diophantine applications
eem2017
Géométrie d'Arakelov et applications diophantiennes
local distribution

We show how to use the recent work of D. McKinnon and M. Roth on generalizations of Diophantine approximation to algebraic varieties to formulate a local version of the Batyrev-Manin principle on the distribution of rational points. We present several toric varieties for which the result is known.