In the original version of this article, there was a gap in the proof of Theorem 38: B as defined does not necessarily have surjective determinant. Thus X_B won't necessarily be defined over Q. We have revised the proof to correct this. The updated version of the paper available at https://arxiv.org/abs/2311.07740 includes a new "descent lemma" prior to the proof of Theorem 38, and it is now used in the subsequent proof.