Lemma 59.78.2. Let $f : X \to Y$ be a quasi-compact and quasi-separated morphism of schemes.

If $\mathcal{F}$ is a torsion abelian sheaf on $X_{\acute{e}tale}$, then $R^ nf_*\mathcal{F}$ is a torsion abelian sheaf on $Y_{\acute{e}tale}$ for all $n$.

If $K$ in $D^+(X_{\acute{e}tale})$ has torsion cohomology sheaves, then $Rf_*K$ is an object of $D^+(Y_{\acute{e}tale})$ whose cohomology sheaves are torsion abelian sheaves.

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