Density of rational points on an algebraic group. (Densité des points rationnels sur un groupe algébrique.)
We obtain upper bound for the density of rational points on the cyclic covers of . As our estimate tends to the conjectural bound of Serre.
We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.