On some arithmetic questions of reductive groups over algebraic extensions of local and global fields

Abstract

In this paper we extend to algebraic extensions of local and global fields and their completions some classical results due to Borel-Serre, Tits, Conrad, Douai, Kneser and Sansuc concerning the finiteness, the surjectivity of maps between Galois cohomology groups and the obstruction to weak approximation and some related results of connected linear algebraic groups.