---
date: 2022-04-18 12:05
modification date: Monday 18th April 2022 12:05:11
title: "open subscheme"
aliases: [open subscheme]
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Last modified date: <%+ tp.file.last_modified_date() %>

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- Tags: 
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- Refs:
	- #todo/add-references
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# open subscheme

An **open subscheme** of $\left(X, \mathscr{O}_{X}\right)$ is a scheme $\left(U, \mathscr{O}_{U}\right)$ whose underlying space is an open subset of $X$ and whose structure sheaf is isomorphic to $\left.\mathscr{O}_{X}\right|_{U}$.

Warning: this definition does not work for a [closed subscheme](closed%20subscheme).