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About: Formally smooth map     Goto   Sponge   NotDistinct   Permalink

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In algebraic geometry and commutative algebra, a ring homomorphism is called formally smooth (from French: Formellement lisse) if it satisfies the following infinitesimal lifting property: Suppose B is given the structure of an A-algebra via the map f. Given a commutative A-algebra, C, and a nilpotent ideal , any A-algebra homomorphism may be lifted to an A-algebra map . If moreover any such lifting is unique, then f is said to be formally étale. Formally smooth maps were defined by Alexander Grothendieck in Éléments de géométrie algébrique IV.