The Stacks project

Example 78.7.6 (Constant group algebraic space). Let $B \to S$ as in Section 78.3. Let $G$ be an abstract group. Consider the functor which associates to any scheme $T$ over $B$ the group of locally constant maps $T \to G$ (where $T$ has the Zariski topology and $G$ the discrete topology). This is representable by the group algebraic space

\[ G_ B = B \times _ S G_ S \]

over $B$. Here $G_ S$ is the constant group scheme introduced in Groupoids, Example 39.5.6.

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