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arXiv · 2506.02600

Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem

Lucas Lagarde
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Abstract

We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we use the obtained description of the unramified Brauer group in order to study the Brauer-Manin obstruction to weak approximation on $X$. In particular, we provide an algorithm to compute the Brauer-Manin obstruction on $X$, which guarantees effectivity of the Grunwald problem for supersolvable groups thanks to previous work of Harpaz and Wittenberg.

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Lucas Lagarde. 2025-06-03. Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem. https://arxiv.org/abs/2506.02600

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