Grothendieck existence theorem

In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), 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.

• Chow's lemma

• "Rigid-analytic geometry and the uniformization of abelian varieties". Snowbird Lectures in Algebraic Geometry. Contemporary Mathematics. Vol. 388. 2005. doi:10.1090/CONM/388. ISBN 9780821837191.

• Mathew, Akhil. "Étale π₁ OF A SMOOTH CURVE" (PDF).
• "Formal Gaga on Artin Stacks" (PDF). 2005. S2CID 296658.

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