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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 29th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: ## Idea A morphism of [[schemes]] (and more general objects, e.g., stacks) that is [[quasicompact]] and [[quasiseparated]]. ## An analogue of good covers for quasicompact quasiseparated schemes Quasicompact quasiseparated schemes are characterized by a property that they admit an analogue (of sorts) of a [[good cover]]: such schemes are precisely those schemes that can be covered by finitely many affine opens such that the intersection of any two opens can itself be covered by finitely many affine opens. ## Related concepts * [[quasicompact morphism]], [[quasiseparated morphism]] * [[good cover]] ## References * [[Ravi Vakil]], [[The Rising Sea]], 5.1.2. <a href="https://ncatlab.org/nlab/revision/quasicompact+quasiseparated+morphism/1">v1</a>, <a href="https://ncatlab.org/nlab/show/quasicompact+quasiseparated+morphism">current</a>

   Created:

   Idea

   A morphism of schemes (and more general objects, e.g., stacks) that is quasicompact and quasiseparated.

   An analogue of good covers for quasicompact quasiseparated schemes

   Quasicompact quasiseparated schemes are characterized by a property that they admit an analogue (of sorts) of a good cover: such schemes are precisely those schemes that can be covered by finitely many affine opens such that the intersection of any two opens can itself be covered by finitely many affine opens.

   Related concepts

   • quasicompact morphism, quasiseparated morphism

   • good cover

   References

   • Ravi Vakil, The Rising Sea, 5.1.2.

   v1, current