Local-global principle for triangularizability and diagonalizability of matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910016091455488 |
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| author | Huang, Kai Liu, Yufan |
| author_facet | Huang, Kai Liu, Yufan |
| contents | Given a number field $k$ with the ring of integers $\mathcal{O}_k$ and a matrix $M\in \mathrm{M}_{n}(\mathcal{O}_k)$. We prove that if $\mathcal{O}_k$ is a principal ideal domain, the local-global principle for triangularizability and diagonalizability of $M$ holds. To explain the possible failures of the local-global principle, we prove that the stratified Brauer--Manin obstruction is the only obstruction to the local-global principle for triangularizability and diagonalizability of $M$ in some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local-global principle for triangularizability and diagonalizability of matrices Huang, Kai Liu, Yufan Number Theory Algebraic Geometry 14G12 (Primary) 15A20 (Secondary) Given a number field $k$ with the ring of integers $\mathcal{O}_k$ and a matrix $M\in \mathrm{M}_{n}(\mathcal{O}_k)$. We prove that if $\mathcal{O}_k$ is a principal ideal domain, the local-global principle for triangularizability and diagonalizability of $M$ holds. To explain the possible failures of the local-global principle, we prove that the stratified Brauer--Manin obstruction is the only obstruction to the local-global principle for triangularizability and diagonalizability of $M$ in some special cases. |
| title | Local-global principle for triangularizability and diagonalizability of matrices |
| topic | Number Theory Algebraic Geometry 14G12 (Primary) 15A20 (Secondary) |
| url | https://arxiv.org/abs/2511.15827 |