Definition 59.23.1. On any of the sites $(\mathit{Sch}/S)_\tau $ or $S_\tau $ of Section 59.20.

The sheaf $T \mapsto \Gamma (T, \mathcal{O}_ T)$ is denoted $\mathcal{O}_ S$, or $\mathbf{G}_ a$, or $\mathbf{G}_{a, S}$ if we want to indicate the base scheme.

Similarly, the sheaf $T \mapsto \Gamma (T, \mathcal{O}^*_ T)$ is denoted $\mathcal{O}_ S^*$, or $\mathbf{G}_ m$, or $\mathbf{G}_{m, S}$ if we want to indicate the base scheme.

The

*constant sheaf*$\underline{\mathbf{Z}/n\mathbf{Z}}$ on any site is the sheafification of the constant presheaf $U \mapsto \mathbf{Z}/n\mathbf{Z}$.

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