Descent obstruction is equivalent to étale Brauer–Manin obstruction

Abstract

Let X be a projective variety over a number field. Completing earlier work of D. Harari, C. Demarche and M. Stoll, we prove that the obstruction to the Hasse principle and weak approximation on X given by descent on torsors under linear algebraic groups is equivalent to the Brauer–Manin obstruction applied to etale covers of X.