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

Algebraic geometry