Geodesic
Boundedness of the p-primary torsion of the Brauer group of products of varieties
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e134

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Skorobogatov, Alexei. Boundedness of the p-primary torsion of the Brauer group of products of varieties. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e134. doi: 10.1017/fms.2025.10078
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