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arXiv · 2512.01014

The \'{e}tale Brauer-Manin obstruction for classifying stacks

Ajneet Dhillon·Nicole Lemire·Jonathan Martin·Yidi Wang
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Abstract

We study the strong approximation for classifying stacks $BG$, where $G$ is a linear algebraic group over a number field $k$. More specifically, we prove that the \'etale Brauer-Manin obstruction is the only obstruction to strong approximation for $BG$. To prove the result, we formulate the theory of torsors and Galois twists for algebraic stacks.

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Ajneet Dhillon, Nicole Lemire, Jonathan Martin, Yidi Wang. 2025-11-30. The \'{e}tale Brauer-Manin obstruction for classifying stacks. https://arxiv.org/abs/2512.01014

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