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arXiv · 1604.03386

Approximation forte pour les vari\'et\'es avec une action d'un groupe lin\'eaire

Yang Cao
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Abstract

Let $G$ be a connected linear algebraic group over a number field. Let $U \hookrightarrow X$ be a $G$-equivariant open embedding of a $G$-homogeneous space with connected stabilizers into a smooth $G$-variety. We prove that $X$ satisfies strong approximation with Brauer-Manin condition off a set $S$ of places of $k$ under either of the following hypotheses : (i) $S$ is the set of archimedean places; (ii) $S$ is a nonempty finite set and $\bar{k}^{\times}= \bar{k}[X]^{\times}$. The proof builds upon the case $X=U$, which has been the object of several works.

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Yang Cao. 2016-04-12. Approximation forte pour les vari\'et\'es avec une action d'un groupe lin\'eaire. https://doi.org/10.1112/s0010437x17007709

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