The Stacks project

Definition 28.21.1. Let $X$ be a scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. We say $\mathcal{F}$ is locally projective if for every affine open $U \subset X$ the $\mathcal{O}_ X(U)$-module $\mathcal{F}(U)$ is projective.