Locally free sheaf

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 pin 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.

ee also

* Swan's theorem

External links

*planetmath|id=4618|title=Locally free


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