SFU NTAG Seminar: Yixin Chen

The Brauer–Manin obstruction provides a powerful framework for explaining failures of the Hasse principle for rational points on algebraic varieties. While many known examples arise from the algebraic part of the Brauer group, comparatively few explicit constructions exhibit genuinely transcendental obstructions.

In this talk, we will present a concrete example of a transcendental Brauer–Manin obstruction to the existence of rational points on a $K3$ surface. We will use a hyperelliptic fibered surface that is birational to this $K3$ surface to help construct the Brauer-Manin obstruction.

This example illustrates how fibration techniques can be used to produce and control transcendental elements in the Brauer group.