Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910982983385088 |
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| author | Lagarde, Lucas |
| author_facet | Lagarde, Lucas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_02600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem Lagarde, Lucas Algebraic Geometry Number Theory 14F22, 14M17, 14G20, 14G25 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. |
| title | Unramified Brauer groups of homogeneous spaces with finite stabilisers and the Grunwald Problem |
| topic | Algebraic Geometry Number Theory 14F22, 14M17, 14G20, 14G25 |
| url | https://arxiv.org/abs/2506.02600 |