Approximation theorems for classifying stacks over number fields

Ajneet Dhillon

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arXiv · 2507.13900

Approximation theorems for classifying stacks over number fields

Ajneet Dhillon

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Abstract

Approximation theorems for algebraic stacks over a number field $k$ are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying stack $BG$. This result answers a very concrete question, given $G$-torsors $P_v$ over $k_v$, where $v$ ranges over a finite number of places, when can you approximate the $P_v$ by a $G$-torsor $P$ defined over $k$.

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Ajneet Dhillon. 2025-07-18. Approximation theorems for classifying stacks over number fields. https://arxiv.org/abs/2507.13900

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