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date: 2022-04-18 12:03
modification date: Monday 18th April 2022 12:03:26
title: "Noetherian scheme"
aliases: [Noetherian scheme]
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# Noetherian scheme

A scheme $X$ is **locally noetherian** if it can be covered by affine open subschemes Spec $A_{i}$ where each $A_{i}$ is noetherian.

$X$ is **noetherian** if it is locally noetherian and only finitely many Spec $A_{i}$ is needed to cover $X$.