In mathematics, the Grothendieck existence theorem, introduced by , gives conditions that enable one to lift infinitesimal deformations of a scheme to a deformation, and to lift schemes over infinitesimal neighborhoods over a subscheme of a scheme S to schemes over S.
The theorem can be viewed as an instance of (Grothendieck's) formal GAGA. See also Chow's lemma References
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formal GAGA
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formal GAGA