Alladi Ramakrishnan Hall

Brauer group of moduli of parabolic G-bundles

Arijit Dey

IIT Madras

Let $k$ be an algebraically closed field of characteristic zero. We prove that the Brauer group of the moduli stack of stable parabolic $\textnormal{PGL}(r,k)$-bundles with full flag quasi-parabolic structures at an arbitrary parabolic divisor on a curve $X$ coincides with the Brauer group of the smooth locus of
the corresponding coarse moduli space of parabolic $\textnormal{PGL}(r,k)$-bundles. We also compute the Brauer group of the smooth locus of this coarse moduli for more general quasi-parabolic types and weights satisfying certain conditions. If time permits we will discuss the case when $G= Sp(2r,\mathbb C)$. This is joint work with Indranil Biswas and Sujoy Chakraborty.