Example 99.12.5. Let $X$ be a scheme of finite type over a field $k$, and let $G$ be a group scheme of finite type over $k$ which acts on $X$. Then the dimension of the quotient stack $[X/G]$ is equal to $\dim (X)-\dim (G)$. In particular, the dimension of the classifying stack $BG=[\mathop{\mathrm{Spec}}(k)/G]$ is $-\dim (G)$. Thus the dimension of an algebraic stack can be a negative integer, in contrast to what happens for schemes or algebraic spaces.

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