Definition:Quasi-Coherent Sheaf of Modules

Definition

Let $\struct {X, \OO_X}$ be a ringed space.

Let $\FF$ be a sheaf of modules $\FF$ over $\OO_X$.

Let $\FF$ be such that:

there exists a cover ${\family {U_i} }_{i \mathop \in I}$ of $X$ such that:

$\FF {\restriction U}$ is a sheaf of modules over $\OO_X {\restriction U}$ presented by global sections.

Then $\FF$ is quasi-coherent.

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