Locally free sheaf

A sheaf of $\emptyset _{X}$-modules ${\mathcal {F}}$ on a ringed space $X$ is called locally free if for each point $p\in X$, there is an open neighborhood $U$ of $x$ such that ${\mathcal {F}}|_{U}$ is free as an $\emptyset _{X}|_{U}$-module, or equivalently, ${\mathcal {F}}_{p}$, the stalk of ${\mathcal {F}}$ at $p$, is free as a $(\emptyset _{X})_{p}$-module. If ${\mathcal {F}}_{p}$ is of finite rank $n$, then ${\mathcal {F}}$ is said to be of rank $n.$

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Locally free at PlanetMath.