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摘要翻译：
设X是数域k上连通线性代数群G′的齐次空间，包含一个k-点X。假定G′中x的稳定器是连通的。利用Colliot-Th\'el\'ene最近提出的拟平凡群的概念，我们可以用X=G/H的形式表示X,其中G是拟平凡K-群，H是G的连通K-子群。设S是K的有限位集。应用[B2]的结果，用H的最大复环商T计算了X关于S的弱逼近的缺陷。特别地，我们证明了如果T在k的一个元循环扩张上分裂，则X具有弱逼近性质。我们还证明了任何具有连通稳定器的齐次空间X（不对T作任何假设）具有实逼近性质。
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英文标题：
《The defect of weak approximation for homogeneous spaces. II》
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作者：
Mikhail Borovoi
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by Colliot-Th\'el\`ene, we can represent X in the form X=G/H, where G is a quasi-trivial k-group and H is a connected k-subgroup of G. Let S be a finite set of places of k. Applying results of [B2], we compute the defect of weak approximation for X with respect to S in terms of the biggest toric quotient T of H. In particular, we show that if T splits over a metacyclic extension of k, then X has the weak approximation property. We show also that any homogeneous space X with connected stabilizer (without assumptions on T) has the real approximation property.
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PDF链接：
https://arxiv.org/pdf/0804.4767
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