Approximation de sous-espaces vectoriels de ${\mathbb{R}}^n$ par des sous-espaces rationnels

Abstract

This PhD thesis elaborates on a problem raised by Schmidt in 1967. We study Diophantine exponents for subspaces, which generalize the irrationality measure for real numbers. We construct subspaces with prescribed exponents and demonstrate properties of algebraic independence among certain exponents.

PhD thesis, in French