On Brauer groups of tame stacks

2024/10/08 by Niven Achenjang, Achenjang, Niven · 1 citation
Mathematics · #14A20 (Secondary) #14F22 (Primary) 14D23 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.06217

openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop some general tools for computing the Brauer group of a tame algebraic stack \mathscr X by studying the difference between it and the Brauer group of the coarse space X of \mathscr X. It is our hope that these tools will be used to simplify future computations of Brauer groups of stacks. Informally, we show that Br\mathscr X is often built from Br X and "information about the Picard groups of the fibers of \mathscr X→ X''. Along these lines, we compute, for example, the Brauer group of the moduli stack \mathscr Y(1)_S of elliptic curves, over any regular noetherian \mathbb Z[1/2]-scheme S as well as the Brauer groups of (many) stacky curves (allowing generic stabilizers) over algebraically closed fields.

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