Definition 59.95.1. Let $X$ be a quasi-compact and quasi-separated scheme. The *cohomological dimension of $X$* is the smallest element

such that for any abelian torsion sheaf $\mathcal{F}$ on $X_{\acute{e}tale}$ we have $H^ i_{\acute{e}tale}(X, \mathcal{F}) = 0$ for $i > \text{cd}(X)$. If $X = \mathop{\mathrm{Spec}}(A)$ we sometimes call this the cohomological dimension of $A$.

## Comments (0)

There are also: