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Geometric Brauer residue via root stacks

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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 the residue of the Brauer class associated to a conic bundle.

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Author's contributions

I would like to thank my advisor Andrew Kresch for the inspiration for this note, and for assisting me tirelessly with the technical details. I would also like to thank the referee for a thorough reading of the paper and for suggesting helpful changes to the exposition. I am supported by Swiss National Science Foundation Grant 156010.

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  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Jakob Oesinghaus

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  1. Jakob Oesinghaus
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Correspondence to Jakob Oesinghaus.

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Oesinghaus, J. Geometric Brauer residue via root stacks. Res Math Sci 5, 28 (2018). https://doi.org/10.1007/s40687-018-0146-0

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