Transcendental Brauer-Manin Obstruction

Abstract: 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.

The fibration allows for a detailed analysis of the surface's geometric and arithmetic properties. This example illustrates how fibration techniques can be used to produce and control transcendental elements in the Brauer group.

algebraic geometrynumber theory

Audience: researchers in the discipline

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SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca

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