The Stacks project

Example 77.7.2 (Roots of unity as a group algebraic space). Let $B \to S$ as in Section 77.3. Let $n \in \mathbf{N}$. Consider the functor which associates to any scheme $T$ over $B$ the subgroup of $\Gamma (T, \mathcal{O}_ T^*)$ consisting of $n$th roots of unity. This is representable by the group algebraic space

\[ \mu _{n, B} = B \times _ S \mu _{n, S} \]

over $B$. Here $\mu _{n, S}$ is the group scheme of $n$th roots of unity over $S$, see Groupoids, Example 39.5.2.

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