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arXiv · 2504.18293

Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle

Yongqi Liang·Yufan Liu
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Abstract

On varieties defined over number fields, we consider obstructions to the Hasse principle given by subgroups of their Brauer groups. Given an arbitrary pair of non-zero finite abelian groups $B_0\subset B$, we prove the existence of a variety $X$ such that its unramified Brauer group is isomorphic to $B$ and moreover $B_0$ is the smallest subgroup of $B$ that obstructs the Hasse principle. The concerned varieties are normic bundles over the projective line.

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Yongqi Liang, Yufan Liu. 2025-04-25. Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle. https://arxiv.org/abs/2504.18293

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