Example 77.7.5. Let $B \to S$ as in Section 77.3. Let $n \geq 1$. The determinant defines a morphism of group algebraic spaces

\[ \det : \text{GL}_{n, B} \longrightarrow \mathbf{G}_{m, B} \]

over $B$. It is the base change of the determinant morphism over $S$ from Groupoids, Example 39.5.5.

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