Definition 59.96.1 (0F0Z)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 59: Étale Cohomology
Section 59.96: Finite cohomological dimension
Definition 59.96.1 (cite)

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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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