Nagata compactification theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Noetherian_schemes
separated morphisms of finite type |
| gptkbp:citation |
Nagata, M. (1962). Imbedding of an abstract variety in a complete variety. J. Math. Kyoto Univ. 2, 1–10.
|
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
Deligne's work on compactification
|
| https://www.w3.org/2000/01/rdf-schema#label |
Nagata compactification theorem
|
| gptkbp:implies |
existence of compactifications for certain morphisms
|
| gptkbp:influenced |
modern algebraic geometry
|
| gptkbp:namedAfter |
gptkb:Masayoshi_Nagata
|
| gptkbp:publishedIn |
Nagata's paper in 1962
|
| gptkbp:relatedTo |
compactification
proper morphism open immersion |
| gptkbp:state |
Every separated finite type morphism from a Noetherian scheme to a quasi-compact quasi-separated scheme factors as an open immersion followed by a proper morphism.
|
| gptkbp:yearProved |
1962
|
| gptkbp:bfsParent |
gptkb:Hideya_Nagata
|
| gptkbp:bfsLayer |
7
|