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The definition of a '''coherent sheaf''' is given as follows:
"''A '''coherent sheaf''' on a [[ringed space]] <math>(X, \mathcal O_X)</math> is a sheaf <math>\mathcal F</math> satisfying the following two properties:▼
▲A '''coherent sheaf''' on a [[ringed space]] <math>(X, \mathcal O_X)</math> is a sheaf <math>\mathcal F</math> satisfying the following two properties:
<ol type="1">
<li> <math>\mathcal F</math> is of ''finite type'' over <math>\mathcal O_X</math>, that is, every point in <math>X</math> has an [[open neighborhood]] <math>U</math> in <math>X</math> such that there is a surjective morphism <math>\mathcal{O}_X^n|_{U} \to \mathcal{F}|_{U} </math> for some natural number <math>n</math>;</li>
<li> for arbitrary open set <math>U\subseteq X</math>, arbitrary natural number <math>n</math>, and arbitrary morphism <math>\varphi: \mathcal{O}_X^n|_{U} \to \mathcal{F}|_{U} </math> of <math>\mathcal O_X</math>-modules, the kernel of <math>\varphi</math> is of finite type.''"</li></ol>
</ol>''" [[Special:Contributions/2601:200:C082:2EA0:E1A8:CCAE:61A1:827C|2601:200:C082:2EA0:E1A8:CCAE:61A1:827C]] ([[User talk:2601:200:C082:2EA0:E1A8:CCAE:61A1:827C|talk]]) 02:19, 9 February 2023 (UTC)▼
But what does the superscript n mean in the symbol "<math>\mathcal{O}_X^n|_{U}</math>"?
The article does not say, and nothing in the linked article [[ringed space]] uses this notation.
I can guess two distinct possibilities for what "<math>\mathcal{O}_X^n|_{U}</math>" means.
▲
== Bad English and grammar ==
Someone please proofread this article. [[Special:Contributions/2A02:6B6F:E98D:400:9BF:E37:5EAC:CB2C|2A02:6B6F:E98D:400:9BF:E37:5EAC:CB2C]] ([[User talk:2A02:6B6F:E98D:400:9BF:E37:5EAC:CB2C|talk]]) 22:16, 6 February 2025 (UTC)
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