Manin obstruction to strong approximation for homogeneous spaces

By M. Borovoi, C. Demarche. 2009

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For a homogeneous space X (not necessarily principal) of a connected 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-Th\'el\`ene and Xu for homogeneous spaces of simply connected semisimple groups, and our proof uses those results.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6009c87c0eb8af8b33a9373154b177c023055c1a