Sous-groupe de Brauer invariant pour un groupe alg\'ebrique connexe quelconque

Abstract

In this paper, for a smooth variety equiped with an action of a connected algebraic group (not necessary linear), we introduce the notion of invariant Brauer sub-group and the notion of invariant \'etale Brauer-Manin obstruction. Then we prove that this obstruction is equivalent to the \'etale Brauer-Manin obstruction. This extends the main notion and the key result of [C17]. As a corollary, this also extends a result of B. Creutz.