Diophantine approximation and local distribution of rational points

rational points
Diophantine approximation
Arakelov Geometry and diophantine applications
Géométrie d'Arakelov et applications diophantiennes
local distribution

Appears in collection : Summer School 2017 - Arakelov Geometry and diophantine applications

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.