Terminal Resolutions of Brauer Pairs

Abstract

A Brauer pair is a pair (X, α) where X is a 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 Brauer pair (Y, α) is a terminal pair if the Brauer discrepancy of (Y, α) is positive. We show that given a Brauer pair (X, α), there is a terminal pair (Y, α) with a birational morphism Y -> X. In short, any Brauer pair admits a terminal resolution.