JournalscmhVol. 88, No. 1pp. 1–54

Manin obstruction to strong approximation for homogeneous spaces

  • Mikhail Borovoi

    Tel Aviv University, Israel
  • Cyril Demarche

    Université Pierre et Marie Curie - Paris 6, France
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Abstract

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