Local distribution of rational points in flag varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912642498560000 |
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| author | Huang, Zhizhong de Saxcé, Nicolas |
| author_facet | Huang, Zhizhong de Saxcé, Nicolas |
| contents | Given a flag variety $X$ defined over $\mathbb{Q}$ and a point $x$ in $X(\mathbb{R})$, we study approximations to $x$ by points $v$ in $X(\mathbb{Q})$, and show that, with an appropriate rescaling, those approximations equidistribute when $x$ is chosen randomly according to a Lebesgue measure on $X(\mathbb{R})$, or when $x$ is defined over $\mathbb{Q}$ and satisfies some non-degeneracy condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local distribution of rational points in flag varieties Huang, Zhizhong de Saxcé, Nicolas Number Theory Dynamical Systems 14G05, 37A17, 11J83 Given a flag variety $X$ defined over $\mathbb{Q}$ and a point $x$ in $X(\mathbb{R})$, we study approximations to $x$ by points $v$ in $X(\mathbb{Q})$, and show that, with an appropriate rescaling, those approximations equidistribute when $x$ is chosen randomly according to a Lebesgue measure on $X(\mathbb{R})$, or when $x$ is defined over $\mathbb{Q}$ and satisfies some non-degeneracy condition. |
| title | Local distribution of rational points in flag varieties |
| topic | Number Theory Dynamical Systems 14G05, 37A17, 11J83 |
| url | https://arxiv.org/abs/2510.09954 |