Brauertsch fields

2023/05/10 by Krashen, Daniel, Lieblich, Max, Shin, Minseon
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.06464

Abstract

We prove a local-to-global principle for Brauer classes: for any finite collection of non-trivial Brauer classes on a variety over a field of transcendence degree at least 3, there are infinitely many specializations where each class stays non-trivial. This is deduced from a Grothendieck--Lefschetz-type theorem for Brauer groups of certain smooth stacks. This also leads to the notion of a Brauertsch field.

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