Example 100.12.5. 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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