Brauertsch fields

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-...

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Bibliographic Details
Main Authors Krashen, Daniel, Lieblich, Max, Shin, Minseon
Format Journal Article
LanguageEnglish
Published 10.05.2023
Subjects
Mathematics - Algebraic Geometry
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Summary: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.
DOI:10.48550/arxiv.2305.06464