Abstract
LetA→A′ be a regular morphism between two noetherian rings. Then for everyA-algebra of finite typeB, everyA-morphism fromB toA′ can be factorised through aB-algebra of finite typeB′ which is standard (smooth) overA and which is «as smooth as possible» overB (i.e. except above the singular locus ofB overA). This result is a positive answer to one conjecture due to M. Artin.
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