Lemma 38.38.7. Let $p$ be a prime number.

If $A$ is an $\mathbf{F}_ p$-algebra, then $\mathop{\mathrm{colim}}\nolimits _ F A = A^{awn}$.

If $S$ is a scheme over $\mathbf{F}_ p$, then the h sheafification of $\mathcal{O}$ sends a quasi-compact and quasi-separated $X$ to $\mathop{\mathrm{colim}}\nolimits _ F \Gamma (X, \mathcal{O}_ X)$.

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