Odd order Brauer--Manin obstruction on diagonal quartic surfaces

2013/12/21 by Ieronymou, Evis, Skorobogatov, Alexei N. · 2 citations
#11D25 #14F22 #14J28 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1312.6255

Abstract

We determine the odd order torsion subgroup of the Brauer group of diagonal quartic surfaces over the field of rational numbers. We show that a non-constant Brauer element of odd order always obstructs weak approximation but never the Hasse principle.

Cited by

• Wild Brauer classes via prismatic cohomology
• Transcendental Brauer groups of cubic generalised Kummer surfaces

Related

• Odd torsion Brauer elements and arithmetic of diagonal quartic surfaces over number fields
• Diagonal quartic surfaces with a Brauer-Manin obstruction
• Quantitative arithmetic of diagonal degree 2 K3 surfaces
• Odd order obstructions to the Hasse principle on general K3 surfaces
• Diagonal quartic surfaces and transcendental elements of the Brauer group