In this article we establish the arithmetic purity of strong approximation for certain semisimple simply connected linear algebraic groups and their homogeneous spaces over a number field $k$. For instance, for any such group $G$ and for any open subset $U$ of $G$ with ${\mathrm {codim}}(G\setminus U, G)\geqslant 2$, we prove that (i) if $G$ is $k$-simple and $k$-isotropic, then $U$ satisfies strong approximation off any finite number of places; and (ii) if $G$ is the spin group of a non-degenerate quadratic form which is not compact over archimedean places, then $U$ satisfies strong approximation off all archimedean places. As a consequence, we prove that the same property holds for affine quadratic hypersurfaces. Our approach combines a fibration method with subgroup actions developed for induction on the codimension of $G\setminus U$, and an affine linear sieve which allows us to produce integral points with almost-prime polynomial values.

在本文中，我们建立了在数域$ k $上某些半简单简单连接的线性代数群及其齐次空间的强逼近的算术纯度。例如，对于任何这样的基团$ G $和任何开子集$ U $的$ G $与$ {\ mathrm {codim}}（G \ setminus U，G）\ geqslant 2 $，我们证明了（ⅰ）如果$ G $是$ $ķ -simple和$ $ķ -isotropic，然后$ U $满足强近似掉任何有限数量的场所; （ii）如果$ G $是非简并二次形式的自旋群，且该二次群在阿基米德地方并不紧凑，则$ U $满足所有阿基米德地区的近似要求。结果，我们证明仿射二次超曲面具有相同的性质。我们的方法将纤维化方法与为对$ G \ setminus U $的余维进行归纳而开发的子组动作以及仿射线性筛子相结合，仿射线性筛子使我们能够生成具有几乎素数多项式值的积分点。