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Dal'nevostochnyi Matematicheskii Zhurnal, 2009, Volume 9, Number 1-2, Pages 15–23 (Mi dvmg15)  

This article is cited in 1 scientific paper (total in 1 paper)

The defect of weak approximation for homogeneous spaces. II

M. V. Borovoi

Tel Aviv University, School of Mathematical Sciences
Full-text PDF (220 kB) Citations (1)
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Abstract: Let $X$ be a right 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 introduced by Colliot-Thélène, we can represent $X$ in the form $X=H\setminus G$, where $G$ is a quasi-trivial $k$-group and $H\subset G$ is a connected $k$-subgroup.
Let $S$ be a finite set of places of $k$. We compute the defect of weak approximation for $X$ with respect to $S$ in terms of the biggest toric quotient $H^{\rm tor}$ of $H$. In particular, we show that if $H^{\rm tor}$ 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 $H^{\rm tor}$) has the real approximation property.
Key words: linear algebraic groups, homogeneous spaces, weak approximation.
Received: 07.04.2009
Document Type: Article
UDC: 512.743.4
MSC: Primary 11G99; Secondary 11E72, 14M17, 20G30
Language: English
Citation: M. V. Borovoi, “The defect of weak approximation for homogeneous spaces. II”, Dal'nevost. Mat. Zh., 9:1-2 (2009), 15–23
Citation in format AMSBIB
\Bibitem{Bor09}
\by M.~V.~Borovoi
\paper The defect of weak approximation for homogeneous spaces.~II
\jour Dal'nevost. Mat. Zh.
\yr 2009
\vol 9
\issue 1-2
\pages 15--23
\mathnet{http://mi.mathnet.ru/dvmg15}
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  • This publication is cited in the following 1 articles:
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