Manin obstruction to strong approximation for homogeneous spaces

  • Mikhail Borovoi

    Tel Aviv University, Israel
  • Cyril Demarche

    Université Pierre et Marie Curie - Paris 6, France


For a homogeneous space (not necessarily principal) of a connected algebraic group (not necessarily linear) over a number field , we prove a theorem of strong approximation for the adelic points of in the Brauer–Manin set. Namely, for an adelic point of orthogonal to a certain subgroup (which may contain transcendental elements) of the Brauer group of with respect to the Manin pairing, we prove a strong approximation property for away from a finite set of places of . 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.

Cite this article

Mikhail Borovoi, Cyril Demarche, Manin obstruction to strong approximation for homogeneous spaces. Comment. Math. Helv. 88 (2013), no. 1, pp. 1–54

DOI 10.4171/CMH/277