The defect of weak approximation for homogeneous spaces. II
| dc.creator | Borovoi, Mikhail | |
| dc.date | 2008-04-30 | |
| dc.date | 2008-05-10 | |
| dc.date.accessioned | 2026-07-07T09:37:49Z | |
| dc.date.available | 2026-07-07T09:37:49Z | |
| dc.description | Let X be a homogeneous space of a connected linear algebraic group G' over a number field k, containing a k-point x. Assume that the stabilizer of x in G' is connected. Using the notion of a quasi-trivial group, recently introduced by Colliot-Thélène, we can represent X in the form X=G/H, where G is a quasi-trivial k-group and H is a connected k-subgroup of G. Let S be a finite set of places of k. Applying results of [B2], we compute the defect of weak approximation for X with respect to S in terms of the biggest toric quotient T of H. In particular, we show that if T splits over a metacyclic extension of k, then X has the weak approximation property. We show also that any homogeneous space X with connected stabilizer (without assumptions on T) has the real approximation property. | |
| dc.description | 10 pages. A section on metacyclic extensions is added | |
| dc.identifier | https://arxiv.org/abs/0804.4767 | |
| dc.identifier | http://arxiv.org/abs/0804.4767 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160595 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G05, 11E72 | |
| dc.title | The defect of weak approximation for homogeneous spaces. II | |
| dc.type | text |