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Homogeneous spaces of Hilbert type
- Source :
- Int. J. Number Theory, 11 (2015), 397-405
- Publication Year :
- 2013
-
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 preprint 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.<br />Comment: 7 pages, final version, to appear in the International Journal of Number Theory
Details
- Database :
- arXiv
- Journal :
- Int. J. Number Theory, 11 (2015), 397-405
- Publication Type :
- Report
- Accession number :
- edsarx.1304.1872
- Document Type :
- Working Paper