Locally free sheaf

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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 x 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.

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