Definition 59.96.1. Let $f : X \to Y$ be a quasi-compact and quasi-separated morphism of schemes. The *cohomological dimension of $f$* is the smallest element

\[ \text{cd}(f) \in \{ 0, 1, 2, \ldots \} \cup \{ \infty \} \]

such that for any abelian torsion sheaf $\mathcal{F}$ on $X_{\acute{e}tale}$ we have $R^ if_*\mathcal{F} = 0$ for $i > \text{cd}(f)$.

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