Brauer Group of Moduli Spaces of PGL(r)-Bundles over a curve

TL;DR

This paper calculates the Brauer group of the moduli stack of stable PGL(r)-bundles over a curve and shows its equivalence with the Brauer group of the smooth locus of the associated coarse moduli space.

Contribution

It provides the first explicit computation of the Brauer group for these moduli stacks and establishes its equality with that of the smooth locus of the coarse moduli space.

Findings

Brauer group of the moduli stack is computed explicitly.

The Brauer group of the stack coincides with that of the smooth locus of the coarse moduli space.

Results are valid over algebraically closed fields of characteristic zero.

Abstract

We compute the Brauer group of the moduli stack of stable PGL(r)-bundles on a curve $X$ over an algebraically closed field of characteristic zero. We also show that the Brauer group of such a moduli stack coincides with the Brauer group of the smooth locus of the corresponding coarse moduli space of stable PGL(r)-bundles on $X$.