Brauer group of moduli stack of stable parabolic $\textnormal{PGL}(r)$-bundles over a curve

Indranil Biswas; Sujoy Chakraborty; Arijit Dey

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arXiv · 2205.12860

Brauer group of moduli stack of stable parabolic $\textnormal{PGL}(r)$-bundles over a curve

Indranil Biswas·Sujoy Chakraborty·Arijit Dey

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Abstract

Let $k$ be an algebraically closed field of characteristic zero. We prove that the Brauer group of 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.

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Indranil Biswas, Sujoy Chakraborty, Arijit Dey. 2022-05-25. Brauer group of moduli stack of stable parabolic $\textnormal{PGL}(r)$-bundles over a curve. https://arxiv.org/abs/2205.12860

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