Homogeneous spaces of Hilbert type

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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
Issue number2
StatePublished - 25 Mar 2015


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


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