Une formule pour le groupe de Brauer algébrique dʼun torseur

Given a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a complex of Galois modules of length 3 and a canonical isomorphism between a hypercohomology group of this complex and an explicit subgroup of the Brauer group of X. This result is obtained as a consequence of a formula describing the “algebraic Brauer group of a torsor”, and it generalizes recent results by Borovoi and van Hamel, by considering non-linear groups G and by taking into account some transcendental elements in the Brauer group of X.