Let $M$ be a DM stack over a field $k$. Assume I managed to represent it as $[X/G]$ for some scheme $X$ and a group scheme $G$. Does that imply that the DM compactification $\overline{M}$ of $M$ is also a global quotient? If yes, how does one prove that? If no, what are natural counterexamples?
2026-03-25 17:26:34.1774459594
representing compactified stack as a global quotient
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