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arXiv · 2107.08906

Local-global principles for homogeneous spaces of reductive groups over global function fields

Cyril Demarche·David Harari
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Abstract

Let $K$ be a global field of positive characteristic. We prove that the Brauer-Manin obstructions to the Hasse principle, to weak approximation and to strong approximation are the only ones for homogeneous spaces of reductive groups with reductive stabilizers. The methods involve abelianization techniques and arithmetic duality theorems for complexes of tori over K.

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Cyril Demarche, David Harari. 2021-07-19. Local-global principles for homogeneous spaces of reductive groups over global function fields. https://arxiv.org/abs/2107.08906

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