Experiments with the transcendental Brauer-Manin obstruction

TL;DR

This paper explores the effectiveness of the transcendental Brauer-Manin obstruction in explaining failures of weak approximation on special Kummer surfaces through experiments and theoretical analysis.

Contribution

It provides new experimental data and theoretical insights into the role of the transcendental Brauer-Manin obstruction for certain algebraic surfaces.

Findings

Transcendental Brauer-Manin obstruction can explain some failures of weak approximation.

Experimental results support theoretical predictions about Kummer surfaces.

New methods developed for analyzing the transcendental Brauer group.

Abstract

We report on our experiments and theoretical investigations concerning weak approximation and the transcendental Brauer-Manin obstruction for special Kummer surfaces.