Groupes arithm\'etiques et approximation diophantienne

Abstract

We develop a theory of diophantine approximation on generalized flag varieties, varieties that can be obtained as a quotient of a semisimple algebraic group by a parabolic subgroup. Using methods from the theory of arithmetic groups, due in particular to Borel and Harish-Chandra, and to Margulis and his collaborators, we prove in this setting analogs of the classical theorems of diophantine approximation.