Vanishing of algebraic Brauer-Manin obstructions

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Abstract

Let X be a homogeneous space of a quasi-trivial k-group G, with geometric stabilizer H, over a number field k. We prove that under certain conditions on the character group of H, certain algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation vanish, because the abelian groups where they take values vanish. When H is connected or abelian, these algebraic Brauer-Manin obstructions to the Hasse principle and weak approximation are the only ones, so we prove the Hasse principle and weak approximation for X under certain conditions. As an application, we obtain new sufficient conditions for the Hasse principle and weak approximation for linear algebraic groups.

Original languageEnglish
Pages (from-to)333-349
Number of pages17
JournalJournal of the Ramanujan Mathematical Society
Volume26
Issue number3
StatePublished - Sep 2011

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