Boundedness of the p-primary torsion of the Brauer groups of K3 surfaces

2024/07/10 by Lazda, Christopher D., Skorobogatov, Alexei N.
#14F22 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.07989

Abstract

We prove that the transcendental Brauer group of a K3 surface X over a finitely generated field k is finite, unless k has positive characteristic p and X is supersingular, in which case it is annihilated by p.

Related

• Boundedness of the p-primary torsion of the Brauer group of products of varieties
• Finiteness of Brauer groups of K3 surfaces in characteristic 2
• Explicit bounds on the transcendental Brauer group of K3 surfaces with principal complex multiplication
• p-Primary Torsion of the Brauer Group in Characteristic p
• Failure of the Hasse principle on general K3 surfaces