The Brauer-Manin obstruction on a general diagonal quartic surface

TL;DR

This paper demonstrates that for a broad class of diagonal quartic surfaces, the Brauer group is non-trivial yet does not prevent the existence of rational points, challenging previous assumptions about obstructions.

Contribution

It establishes that the Brauer-Manin obstruction does not account for the absence of rational points on general diagonal quartic surfaces.

Findings

Non-trivial Brauer group on general diagonal quartic surfaces

No Brauer-Manin obstruction to rational points

Existence of rational points despite non-trivial Brauer group

Abstract

We prove that, on a sufficiently general diagonal quartic surface, there is a non-trivial Brauer group but no Brauer-Manin obstruction to the existence of rational points.