The Stacks project

Example 78.7.1 (Multiplicative group algebraic space). Let $B \to S$ as in Section 78.3. Consider the functor which associates to any scheme $T$ over $B$ the group $\Gamma (T, \mathcal{O}_ T^*)$ of units in the global sections of the structure sheaf. This is representable by the group algebraic space

\[ \mathbf{G}_{m, B} = B \times _ S \mathbf{G}_{m, S} \]

over $B$. Here $\mathbf{G}_{m, S}$ is the multiplicative group scheme over $S$, see Groupoids, Example 39.5.1.

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View Example 78.7.1 as pdf