Example 76.52.2. Let $k$ be a field. Let $X$ be an algebraic space of finite presentation over $k$ (in particular $X$ is quasi-compact). Then an object $E$ of $D(\mathcal{O}_ X)$ is $k$-perfect if and only if it is bounded and pseudo-coherent (by definition), i.e., if and only if it is in $D^ b_{\textit{Coh}}(X)$ (by Derived Categories of Spaces, Lemma 75.13.7). Thus being relatively perfect does not mean “perfect on the fibres”.
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