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Locally free sheaf - Wikipedia, the free encyclopedia

Locally free sheaf

From Wikipedia, the free encyclopedia

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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 $n .$

[edit] See also

Swan's theorem

[edit] External link

This article incorporates material from Locally free on PlanetMath, which is licensed under the GFDL.

Retrieved from "http://en.wikipedia.org../../../l/o/c/Locally_free_sheaf.html"

Categories: PlanetMath sourced articles | Algebraic geometry | Sheaf theory

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