Groupe de Brauer non ramifi\'e alg\'ebrique des espaces homog\`enes (The unramified algebraic Brauer group of homogeneous spaces)

Abstract

Using a reduction of the Galois cohomology of a linear algebraic group $G$ to that of a certain finite subquotient, we give different formulas allowing the calculation of the unramified algebraic Brauer group of a homogeneous space $V=G\backslash G'$ with $G'$ semisimple and simply connected, both over a finite field and over an arbitrary field of characteristic $0$.