Example 77.7.4 (General linear group algebraic space). Let $B \to S$ as in Section 77.3. Let $n \geq 1$. Consider the functor which associates to any scheme $T$ over $B$ the group

$\text{GL}_ n(\Gamma (T, \mathcal{O}_ T))$

of invertible $n \times n$ matrices over the global sections of the structure sheaf. This is representable by the group algebraic space

$\text{GL}_{n, B} = B \times _ S \text{GL}_{n, S}$

over $B$. Here $\mathbf{G}_{m, S}$ is the general linear group scheme over $S$, see Groupoids, Example 39.5.4.

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