Boundedness of the p-primary torsion of the Brauer group of products of varieties
Author(s)
Skorobogatov, Alexei
Type
Journal Article
Abstract
Let k be a field finitely generated over its prime subfield. We prove that the quotient of the Brauer group of a product of varieties over k by the sum of the images of the Brauer groups of factors has finite exponent. The bulk of the proof concerns p-primary torsion in characteristic p. Our approach gives a more direct proof of the boundedness of the p-primary torsion of the Brauer group of an abelian variety, as recently proved by D’Addezio. We show that the transcendental Brauer group of a Kummer surface over k has finite exponent but can be infinite when k is an infinite field of positive characteristic. This answers a question of Zarhin and the author.
Date Issued
2025-08-14
Date Acceptance
2025-06-02
Citation
Forum of Mathematics, Sigma, 2025, 13
ISSN
2050-5094
Publisher
Cambridge University Press
Journal / Book Title
Forum of Mathematics, Sigma
Volume
13
Copyright Statement
© The Author(s), 2025. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Subjects
DESCENT
FINITENESS THEOREM
K3 SURFACES
Mathematics
Mathematics, Applied
Physical Sciences
Science & Technology
Publication Status
Published
Article Number
e134
Date Publish Online
2025-08-14