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Formally étale morphism : ウィキペディア英語版
Formally étale morphism
In commutative algebra and algebraic geometry, a morphism is called formally étale if has a lifting property that is analogous to being a local diffeomorphism.
== Formally étale homomorphisms of rings ==
Let ''A'' be a topological ring, and let ''B'' be a topological ''A''-algebra. ''B'' is formally étale if for all discrete ''A''-algebras ''C'', all nilpotent ideals ''J'' of ''C'', and all continuous ''A''-homomorphisms , there exists a unique continuous ''A''-algebra map such that , where is the canonical projection.〔EGA 0IV, Définition 19.10.2.〕
Formally étale is equivalent to formally smooth plus formally unramified.〔EGA 0IV, Définition 19.10.2.〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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