Existence of terminal resolutions of geometric Brauer pairs of arbitrary dimension

A geometric Brauer pair is a pair (X,α) where X is a smooth quasi-projective variety over an algebraically closed field and α is an element in the 2-torsion part of the Brauer group of the function field of X. A geometric Brauer pair (Y,α) is a terminal pair if the Brauer discrepancy of (Y,α) is positive. We show that given a geometric Brauer pair (X,α), there is a terminal pair (Y,α) with a birational morphism Y→X. In short, any geometric Brauer pair admits a terminal resolution.