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

Fuente: arXiv
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Main Authors: Liang, Yongqi, Liu, Yufan
Format: Preprint
Published: 2025
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author Liang, Yongqi
Liu, Yufan
author_facet Liang, Yongqi
Liu, Yufan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_18293
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle
Liang, Yongqi
Liu, Yufan
Number Theory
Algebraic Geometry
14G12, 14G05, 14F22
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.
title Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle
topic Number Theory
Algebraic Geometry
14G12, 14G05, 14F22
url https://arxiv.org/abs/2504.18293