A Simpler Approach to a Descent Conjecture of Wittenberg

A descent conjecture of Wittenberg [Wit24, Conjecture 3.7.4] predicts that if all the twists of a rationally connected torsor over a smooth base satisfy weak approximation with Brauer-Manin obstruction, then so does the base. We give an alternative proof of Wittenberg’s conjecture for certain torsors under connected linear groups via Cao’s descent formula.