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arXiv · 2511.00824

On almost strong approximation for linear algebraic groups

Yang Cao·Yijin Wang
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Abstract

Let $G$ be a connected linear algebraic group over a number field $K$. In this article, we study the almost strong approximation property (ASA) of $G$ raised by Rapinchuk and Tralle. Building on Demarche's results on strong approximation with Brauer-Manin obstruction, we introduce a necessary and sufficient condition for (ASA) to hold in terms of the Brauer group of $G$. Using the criteria, we conclude that (ASA) can be completely controlled by the Dirichlet density of the places and the splitting field of $G$, which generalizes a result of Rapinchuk and Tralle.

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Yang Cao, Yijin Wang. 2025-11-02. On almost strong approximation for linear algebraic groups. https://arxiv.org/abs/2511.00824

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