## Abstract

Fora homogeneous spaceX (not necessarily principal)ofaconnected algebraic group G (not necessarily linear) over a number field k, we prove a theorem of strong approximation for the adelic points of X in the Brauer-Manin set. Namely, for an adelic point x of X orthogonal to a certain subgroup (which may contain transcendental elements) of the Brauer group Br.X/of X with respect to the Manin pairing, we prove a strong approximation property for x away from a finite set S of places of k. Our result extends a result of Harari for torsors of semiabelian varieties and a result of Colliot-Thélène and Xu for homogeneous spaces of simply connected semisimple groups, and our proof uses those results.

Original language | English |
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Pages (from-to) | 1-54 |

Number of pages | 54 |

Journal | Commentarii Mathematici Helvetici |

Volume | 88 |

Issue number | 1 |

DOIs | |

State | Published - 2013 |

## Keywords

- Brauer group
- Connected algebraic groups
- Homogeneous spaces
- Manin obstruction
- Strong approximation