Brauer-Manin Obstruction on Generalized Kummer Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917024322551808 |
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| author | Zhu, Eric |
| author_facet | Zhu, Eric |
| contents | Given an abelian variety $A$ over a number field, we consider the generalized Kummer varieties of $A$ coming from quotients of $A$ by an automorphism of prime order $p > 2$. We prove that the Brauer-Manin obstruction on these generalized Kummer varieties only can come from the $p$-primary part of the Brauer group. This is applied to show that certain families of such varieties have no Brauer-Manin obstruction to the local-global principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brauer-Manin Obstruction on Generalized Kummer Varieties Zhu, Eric Number Theory Given an abelian variety $A$ over a number field, we consider the generalized Kummer varieties of $A$ coming from quotients of $A$ by an automorphism of prime order $p > 2$. We prove that the Brauer-Manin obstruction on these generalized Kummer varieties only can come from the $p$-primary part of the Brauer group. This is applied to show that certain families of such varieties have no Brauer-Manin obstruction to the local-global principle. |
| title | Brauer-Manin Obstruction on Generalized Kummer Varieties |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.16328 |