Definition 20.42.1. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{E}^\bullet$ be a complex of $\mathcal{O}_ X$-modules. We say $\mathcal{E}^\bullet$ is strictly perfect if $\mathcal{E}^ i$ is zero for all but finitely many $i$ and $\mathcal{E}^ i$ is a direct summand of a finite free $\mathcal{O}_ X$-module for all $i$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).