Local distribution of rational points in flag varieties

Zhizhong Huang; Nicolas de Saxcé

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arXiv · 2510.09954

Local distribution of rational points in flag varieties

Zhizhong Huang·Nicolas de Saxcé

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Abstract

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.

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Zhizhong Huang, Nicolas de Saxcé. 2025-10-11. Local distribution of rational points in flag varieties. https://arxiv.org/abs/2510.09954

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