Transcendental Brauer-Manin obstruction on a pencil of elliptic curves

Abstract

This note gives an explicit example of transcendental Brauer-Manin obstruction to weak approximation. It has two features which the only previously known example of such obstruction did not have: the class in the Brauer group which is responsible for the obstruction is divisible, and the underlying algebraic variety is an elliptic surface (a K3 surface).

5 pages; old paper (2003), posted for archival purposes

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• Brauer-Manin obstructions to integral points
• A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold