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Example 78.7.3 (Additive 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 global sections of the structure sheaf. This is representable by the group algebraic space

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

over $B$. Here $\mathbf{G}_{a, S}$ is the additive group scheme over $S$, see Groupoids, Example 39.5.3.

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