PlanetMath: closed immersion

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closed immersion

(Definition)

A morphism of schemes $f: (X,\O _X) \longrightarrow (Y,\O _Y)$ is a closed immersion if:

As a map of topological spaces, $f: X \longrightarrow Y$ is a homeomorphism from into a closed subset of , and
the morphism of sheaves $\O _Y \longrightarrow \O _X$ associated with is an epimorphism in the category of sheaves.

This notion is the analog of the notion of closed immersion in the category of differential manifolds.

"closed immersion" is owned by djao. [ full author list (2) ]

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Cross-references: differential manifolds, sheaves, category, morphism of sheaves, closed subset, homeomorphism, topological spaces, map, morphism of schemes
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This is version 3 of closed immersion, born on 2002-07-14, modified 2004-03-30.
Object id is 3165, canonical name is ClosedImmersion.
Accessed 2661 times total.

Classification:

14A15 (Algebraic geometry :: Foundations :: Schemes and morphisms)

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