A cohomological obstruction to weak approximation for homogeneous spaces

Mikhail Borovoi; Tomer M. Schlank

doi:10.17323/1609-4514-2012-12-1-1-20

A cohomological obstruction to weak approximation for homogeneous spaces

Mikhail Borovoi^*, Tomer M. Schlank

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 ⊂ 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.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Moscow Mathematical Journal
Volume	12
Issue number	1
DOIs	https://doi.org/10.17323/1609-4514-2012-12-1-1-20
State	Published - 2012

Keywords

Brauer group
Brauer-Manin obstruction
Galois cohomology
Homogeneous spaces
Linear algebraic groups
Weak approximation

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10.17323/1609-4514-2012-12-1-1-20

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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 ⊂ 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.",

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AB - Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k and H ⊂ 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.

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KW - Brauer-Manin obstruction

KW - Galois cohomology

KW - Homogeneous spaces

KW - Linear algebraic groups

KW - Weak approximation

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A cohomological obstruction to weak approximation for homogeneous spaces

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Keywords

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