Diagonal quartic surfaces and transcendental elements of the Brauer group

2009/11/06 by Evis Ieronymou, Ieronymou, Evis · 1 citation
Mathematics · #11G #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0911.1268

openalex publication_date 2009/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group. We investigate whether the 2-primary part of the Brauer group of a diagonal quartic surface over a number field is algebraic and give sufficient conditions for this to be the case. In the last section we give an obstruction to weak approximation due to a transendental class on a specific diagonal quartic surface, an obstruction which cannot be explained by the algebraic Brauer group which in this case is just the constant algebras.

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• Wild Brauer classes via prismatic cohomology

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