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
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AN - SCOPUS:84928586112
SN - 1793-0421
VL - 11
SP - 397
EP - 405
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 2
ER -