A sheaf of $\O_X$ -modules $\F$ 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 $\F|_U$ is free as an $\O_X|_U$ -module, or equivalently, $\F_p$ , the stalk of $\F$ at $p$ , is free as a $(\O_X)_p$ -module. If $\F_p$ is of finite rank $n$ , then $\F$ is said to be of rank $n$ .