Brauer group of moduli of torsors under Bruhat–Tits group scheme GG over a curve

Abstract

Let X be a smooth projective curve over C. We compute the Brauer group of the moduli stack MX(G) of Bruhat–Tits group scheme G-torsors. Let MrsX(G) denote the regularly stable locus of the coarse moduli space of semi-stable G-torsors. When g(X)≥3, we compute the kernel of Br(MrsX(G))→Br(MX(G)).