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- Stein_factorization abstract "In algebraic geometry, the Stein factorization, introduced by Karl Stein (1956) for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a mapping to points.One version for schemes states the following:(EGA, III.4.3.1)Let X be a scheme, S a locally noetherian scheme and a proper morphism. Then one can writewhere is a finite morphism and is a proper morphism so that .The existence of this decomposition itself is not difficult. (see below) But, by Zariski's connectedness theorem, the last part in the above says that the fiber is connected for any . It follows:Corollary: For any , the set of connected components of the fiber is in bijection with the set of points in the fiber .".
- Stein_factorization wikiPageExternalLink the-baby-version-of-zariskis-main-theorem.
- Stein_factorization wikiPageID "1205940".
- Stein_factorization wikiPageRevisionID "595883638".
- Stein_factorization authorlink "Karl Stein".
- Stein_factorization first "Karl".
- Stein_factorization hasPhotoCollection Stein_factorization.
- Stein_factorization last "Stein".
- Stein_factorization year "1956".
- Stein_factorization subject Category:Algebraic_geometry.
- Stein_factorization comment "In algebraic geometry, the Stein factorization, introduced by Karl Stein (1956) for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a mapping to points.One version for schemes states the following:(EGA, III.4.3.1)Let X be a scheme, S a locally noetherian scheme and a proper morphism.".
- Stein_factorization label "Stein factorization".
- Stein_factorization sameAs m.0l8m_1w.
- Stein_factorization sameAs Q7606788.
- Stein_factorization sameAs Q7606788.
- Stein_factorization wasDerivedFrom Stein_factorization?oldid=595883638.
- Stein_factorization isPrimaryTopicOf Stein_factorization.