Grothendieck existence theorem explained

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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• 10.1090/S0002-9947-1991-1014252-X. Grothendieck's existence theorem in analytic geometry and related results . 1991 . Kosarew . Siegmund . Transactions of the American Mathematical Society . 328 . 1 . 259–306 . free. 2001883 .
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• 10.1016/j.aim.2004.08.017 . free . On proper coverings of Artin stacks . 2005 . Olsson . Martin C. . . 198 . 1 . 93–106 .

formal GAGA

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

External links

• Web site: 30.24 Grothendieck's existence theorem, I. The Stacks Project authors .
• Web site: 75.42 Grothendieck's existence theorem. The Stacks Project authors .
• Web site: Grothendieck's existence theorem in formal geometry (Advanced School in Basic Algebraic Geometry | (smr 1487)). L.. ILLUSIE. 7–18 July 2003. The Abdus Salam International Centre for Theoretical Physics. Trieste - Italy.

formal GAGA

• Web site: Mathew . Akhil . Étale π₁ OF A SMOOTH CURVE.
• Web site: Formal Gaga on Artin Stacks . 296658 . 2005 .