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locally free
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(Definition)
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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 $n$ .
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"locally free" is owned by mps. [ full author list (3) | owner history (2) ]
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Cross-references: stalk, open, point, ringed space, sheaf
There are 5 references to this entry.
This is version 10 of locally free, born on 2003-08-19, modified 2005-10-20.
Object id is 4618, canonical name is LocallyFree.
Accessed 2944 times total.
Classification:
| AMS MSC: | 14A99 (Algebraic geometry :: Foundations :: Miscellaneous) |
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Pending Errata and Addenda
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