The étale Brauer-Manin obstruction for classifying stacks

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 étale 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.

15 pages; minor changes in Section 3. Comments welcome!