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- Radicial_morphism abstract "In algebraic geometry, a morphism of schemesf: X → Yis called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective. (EGA I, (3.5.4)) This is a generalization of the notion of a purely inseparable extension of fields (sometimes called a radicial extension, which should not be confused with a radical extension.)It suffices to check this for K algebraically closed.This is equivalent to the following condition: f is injective on the topological spaces and for every point x in X, the extension of the residue fieldsk(f(x)) ⊂ k(x)is radicial, i.e. purely inseparable.It is also equivalent to every base change of f being injective on the underlying topological spaces. (Thus the term universally injective.)Radicial morphisms are stable under composition, products and base change. If gf is radicial, so is f.".
- Radicial_morphism wikiPageExternalLink feuilleter?id=PMIHES_1960__4_.
- Radicial_morphism wikiPageID "14483490".
- Radicial_morphism wikiPageLength "1842".
- Radicial_morphism wikiPageOutDegree "12".
- Radicial_morphism wikiPageRevisionID "607162784".
- Radicial_morphism wikiPageWikiLink Algebraic_geometry.
- Radicial_morphism wikiPageWikiLink Category:Morphisms_of_schemes.
- Radicial_morphism wikiPageWikiLink Injective.
- Radicial_morphism wikiPageWikiLink Injective_function.
- Radicial_morphism wikiPageWikiLink Morphism.
- Radicial_morphism wikiPageWikiLink Publications_Mathxc3xa9matiques_de_lIHxc3x89S.
- Radicial_morphism wikiPageWikiLink Purely_inseparable_extension.
- Radicial_morphism wikiPageWikiLink Purely_inseparable_field_extension.
- Radicial_morphism wikiPageWikiLink Radical_extension.
- Radicial_morphism wikiPageWikiLink Radicial_extension.
- Radicial_morphism wikiPageWikiLink Residue_field.
- Radicial_morphism wikiPageWikiLink Scheme_(mathematics).
- Radicial_morphism wikiPageWikiLink Springer-Verlag.
- Radicial_morphism wikiPageWikiLink Springer_Science+Business_Media.
- Radicial_morphism wikiPageWikiLinkText "Radicial morphism".
- Radicial_morphism wikiPageWikiLinkText "radicial morphism".
- Radicial_morphism wikiPageWikiLinkText "radicial".
- Radicial_morphism hasPhotoCollection Radicial_morphism.
- Radicial_morphism wikiPageUsesTemplate Template:Citation.
- Radicial_morphism subject Category:Morphisms_of_schemes.
- Radicial_morphism type Morphism.
- Radicial_morphism comment "In algebraic geometry, a morphism of schemesf: X → Yis called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective.".
- Radicial_morphism label "Radicial morphism".
- Radicial_morphism sameAs m.03d4yqt.
- Radicial_morphism sameAs Q17099707.
- Radicial_morphism sameAs Q17099707.
- Radicial_morphism wasDerivedFrom Radicial_morphism?oldid=607162784.
- Radicial_morphism isPrimaryTopicOf Radicial_morphism.