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Approximation forte pour les variétés avec une action d’un groupe linéaire
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 4 / April 2018
- Published online by Cambridge University Press:
- 08 March 2018, pp. 773-819
- Print publication:
- April 2018
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- Article
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Let
$G$ be a connected linear algebraic group over a number field 
$k$. Let 
$U{\hookrightarrow}X$ be a 
$G$-equivariant open embedding of a 
$G$-homogeneous space 
$U$ with connected stabilizers into a smooth 
$G$-variety 
$X$. 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 non-empty 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.
