Vanishing of Brauer classes on K3 surfaces under reduction

2023/03/29 by Davesh Maulik, Maulik, Davesh, Salim Tayou +1
Mathematics · #11G18 #14F22 #14G35 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.16401

openalex publication_date 2023/03/29 · openalex created_date 2023/04/05 · openalex updated_date 2026/07/28

Abstract

Given a Brauer class on a K3 surface defined over a number field, we prove that there exists infinitely many reductions where the Brauer class vanishes, under certain technical hypotheses, answering a question of Frei--Hassett--Várilly-Alvarado.

Related

• Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence
• Invariants of Vanishing Brauer Classes
• Explicit bounds on the transcendental Brauer group of K3 surfaces with principal complex multiplication
• Persistence of the Brauer-Manin obstruction on cubic surfaces
• Insufficiency of the Brauer-Manin obstruction for Enriques surfaces