Homogeneous spaces of Hilbert type

Mikhail Borovoi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let k be a global field. Let G be a connected linear algebraic k-group, assumed reductive when k is a function field. It follows from a result of a paper by Bary-Soroker, Fehm and Petersen that when H is a smooth connected k-subgroup of G, the quotient space G/H is of Hilbert type. We prove a similar result for certain non-connected k-subgroups H of G. In particular, we prove that if G is a simply connected k-group over a number field k, and H is an abelian k-subgroup of G, not necessarily connected, then G/H is of Hilbert type.

Original languageEnglish
Pages (from-to)397-405
Number of pages9
JournalInternational Journal of Number Theory
Volume11
Issue number2
DOIs
StatePublished - 25 Mar 2015

Funding

FundersFunder number
Hermann Minkowski Center for Geometry

    Keywords

    • Hilbertian field
    • homogeneous space
    • linear algebraic group
    • variety of Hilbert type
    • weak weak approximation

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