Lemma 59.78.1. Let $X$ be a quasi-compact and quasi-separated scheme.

If $\mathcal{F}$ is a torsion abelian sheaf on $X_{\acute{e}tale}$, then $H^ n_{\acute{e}tale}(X, \mathcal{F})$ is a torsion abelian group for all $n$.

If $K$ in $D^+(X_{\acute{e}tale})$ has torsion cohomology sheaves, then $H^ n_{\acute{e}tale}(X, K)$ is a torsion abelian group for all $n$.

## Comments (0)