The Brauer Group of a Smooth Orbifold

TL;DR

This paper investigates the Brauer group of smooth quasiprojective orbifolds over a field and compares it with the Brauer group of the smooth locus of their coarse moduli spaces.

Contribution

It provides a comparison between the Brauer group of a smooth orbifold and that of the smooth locus of its coarse moduli space, offering new insights into their relationship.

Findings

Establishes a relationship between the Brauer groups of orbifolds and their coarse moduli spaces.

Identifies conditions under which the Brauer groups coincide or differ.

Enhances understanding of the Brauer group structure in the context of algebraic stacks.

Abstract

Let $k$ be a field and $X/k$ be a smooth quasiprojective orbifold. Let $X\to \underline{X}$ be its coarse moduli space. In this paper we study the Brauer group of $X$ and compare it with the Brauer group of the smooth locus of $\underline{X}$.