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arXiv · 2511.15827

Local-global principle for triangularizability and diagonalizability of matrices

Kai Huang·Yufan Liu
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Abstract

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.

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Kai Huang, Yufan Liu. 2025-11-19. Local-global principle for triangularizability and diagonalizability of matrices. https://arxiv.org/abs/2511.15827

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