Geometric Brauer residue via root stacks

TL;DR

This paper introduces a geometric approach to the Brauer residue map using root stacks and Weil restriction, providing explicit representatives for residues in the context of conic and Brauer-Severi bundles.

Contribution

It offers a novel geometric reinterpretation of the Brauer residue map through root stacks and Weil restriction, with applications to explicit residue representatives.

Findings

Reinterpreted the Brauer residue map geometrically using root stacks.

Constructed explicit representatives for residues of Brauer classes.

Applied the method to conic and Brauer-Severi bundles.

Abstract

We reinterpret the residue map for the Brauer group of a smooth variety using a root stack construction and Weil restriction for algebraic stacks, and apply the result to find a geometric representative of for the residue of a Brauer class associated to a conic bundle, or more generally a Brauer-Severi bundle.