Groupes de Brauer algébriques modulo les constantes d’espaces homogènes et leurs compactifications - Linh, Nguyen Manh (Comptes Rendus. Mathématique)
Let $X$ be a smooth, geometrically integral variety without non-constant invertible functions over a field $K$. Then the quotient of the “algebraic” Brauer group of $X$ by $Br\,K$ injects into $H^1(K,Pic{\overline{X}})$. We show that this inclusion is not always an isomorphism, even in the case where $X$ is a homogeneous space of a connected linear algebraic group over $K$. A similar result for the smooth compactifications of $X$ is also given.