Lemma 59.63.1. Let $p$ be a prime. Let $S$ be a scheme of characteristic $p$.

If $S$ is affine, then $H_{\acute{e}tale}^ q(S, \underline{\mathbf{Z}/p\mathbf{Z}}) = 0$ for all $q \geq 2$.

If $S$ is a quasi-compact and quasi-separated scheme of dimension $d$, then $H_{\acute{e}tale}^ q(S, \underline{\mathbf{Z}/p\mathbf{Z}}) = 0$ for all $q \geq 2 + d$.

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