The Brauer group of the universal moduli space of vector bundles over smooth curves

Abstract

We compute the Brauer group of the universal moduli stack of vector bundles on (possibly marked) smooth curves of genus at least three over the complex numbers. As consequence, we obtain an explicit description of the Brauer group of the smooth locus of the associated moduli space of semistable vector bundles, when the genus is at least four. Contents 1 Preliminaries about the Brauer group of an Artin stack. 4 1.1 Brauer group, Cohomological Brauer group, Bigger Brauer group . . . . . . . . . 4 1.2 Some invariance results .