The unramified Brauer group of homogeneous spaces with finite stabilizer

Abstract

We give formulas for calculating the unramified Brauer group of a homogeneous space X X of a semisimple simply connected group G G with finite geometric stabilizer F ¯ \bar F over a wide family of fields of characteristic 0 0 . When k k is a number field, we use these formulas in order to study the Brauer–Manin obstruction to the Hasse principle and weak approximation. We prove in particular that the Brauer-Manin pairing is constant on X ( k v ) X(k_v) for every v v outside of an explicit finite set of nonarchimedean places of k k .