Brauer group of moduli of principal bundles over a curve

TL;DR

This paper computes the Brauer groups of the moduli space and stack of semistable principal G-bundles over a smooth complex curve of genus at least three, advancing understanding of their algebraic structure.

Contribution

It provides explicit calculations of the Brauer groups for these moduli spaces and stacks, which were previously unknown.

Findings

Brauer group of the moduli space's smooth locus computed

Brauer group of the moduli stack computed

Results apply to semisimple linear algebraic groups over complex curves

Abstract

Let $G$ be a semisimple linear algebraic group over the field $\mathbb C$, and let $C$ be an irreducible smooth complex projective curve of genus at least three. We compute the Brauer group of the smooth locus of the moduli space of semistable principal $G$--bundles over $C$. We also compute the Brauer group of the moduli stack of principal $G$--bundles over $C$.