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Mosc. Math. J., 2012, Volume 12, Number 1, Pages 1–20 (Mi mmj444)  

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

A cohomological obstruction to weak approximation for homogeneous spaces

Mikhail Borovoia, Tomer M. Schlankb

a Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
b Institute of Mathematics, Hebrew University, Jerusalem, Israel

Abstract: Let $X$ be a homogeneous space, $X=G/H$, where $G$ is a connected linear algebraic group over a number field $k$, and $H\subset G$ is a $k$-subgroup (not necessarily connected). Let $S$ be a finite set of places of $k$. We compute a Brauer–Manin obstruction to weak approximation for $X$ in $S$ in terms of Galois cohomology.

Key words and phrases: Brauer–Manin obstruction, weak approximation, homogeneous spaces, linear algebraic groups, Brauer group, Galois cohomology.

DOI: https://doi.org/10.17323/1609-4514-2012-12-1-1-20

Full text: http://www.ams.org/.../abst12-1-2012.html
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MSC: Primary 14M17; Secondary 14G05, 20G10, 20G30
Received: January 19, 2011
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Citation: Mikhail Borovoi, Tomer M. Schlank, “A cohomological obstruction to weak approximation for homogeneous spaces”, Mosc. Math. J., 12:1 (2012), 1–20

Citation in format AMSBIB
\Bibitem{BorSch12}
\by Mikhail~Borovoi, Tomer~M.~Schlank
\paper A cohomological obstruction to weak approximation for homogeneous spaces
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 1--20
\mathnet{http://mi.mathnet.ru/mmj444}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-1-20}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952422}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309364900001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. C. Demarche, “The fundamental group of a homogeneous space of a linear algebraic group”, Math. Ann., 368:1-2 (2017), 339–365  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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