TY - JOUR

T1 - Homogeneous spaces of Hilbert type

AU - Borovoi, Mikhail

N1 - Publisher Copyright:
© 2015 World Scientific Publishing Company.

PY - 2015/3/25

Y1 - 2015/3/25

N2 - 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.

AB - 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.

KW - Hilbertian field

KW - homogeneous space

KW - linear algebraic group

KW - variety of Hilbert type

KW - weak weak approximation

UR - http://www.scopus.com/inward/record.url?scp=84928586112&partnerID=8YFLogxK

U2 - 10.1142/S1793042115500207

DO - 10.1142/S1793042115500207

M3 - מאמר

AN - SCOPUS:84928586112

VL - 11

SP - 397

EP - 405

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 2

ER -