Locally free sheaf

In sheaf theory, a field of mathematics, a sheaf of ${\mathcal {O}}_{X}$ -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 $p$ such that ${\mathcal {F}}|_{U}$ is free as an ${\mathcal {O}}_{X}|_{U}$ -module, or equivalently, ${\mathcal {F}}_{p}$ , the stalk of ${\mathcal {F}}$ at $p$ , is free as a $({\mathcal {O}}_{X})_{p}$ -module. If ${\mathcal {F}}_{p}$ is of finite rank $n$ , then ${\mathcal {F}}$ is said to be of rank $n.$