Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10498 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915933384081408 |
|---|---|
| author | Chen, Sheng Huang, Kai |
| author_facet | Chen, Sheng Huang, Kai |
| contents | Given a finite extension $K/k$ of number fields and a smooth quasi-projective variety $X$ over $K$. If the abelianized fundamental group of $X$ is trivial, we prove that there is a natural identification between Brauer-Manin sets of $X$ and its Weil restriction $R_{K/k}X$. If $X$ is projective and $Pic(X\times_{K}\overline{k})$ is a torsion-free abelian group, we prove that there is a natural identification between algebraic Brauer-Manin sets of $X$ and $R_{K/k}X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on Brauer-Manin obstruction for Weil restrictions Chen, Sheng Huang, Kai Number Theory 11G35, 14G05 Given a finite extension $K/k$ of number fields and a smooth quasi-projective variety $X$ over $K$. If the abelianized fundamental group of $X$ is trivial, we prove that there is a natural identification between Brauer-Manin sets of $X$ and its Weil restriction $R_{K/k}X$. If $X$ is projective and $Pic(X\times_{K}\overline{k})$ is a torsion-free abelian group, we prove that there is a natural identification between algebraic Brauer-Manin sets of $X$ and $R_{K/k}X$. |
| title | Remarks on Brauer-Manin obstruction for Weil restrictions |
| topic | Number Theory 11G35, 14G05 |
| url | https://arxiv.org/abs/2604.10498 |