In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, the Grothendieck existence theorem, introduced by , gives conditions that enable one to lift
infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...
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
Chow's lemma, named after Wei-Liang Chow, is one of the foundational results in algebraic geometry. It roughly says that a proper morphism is fairly close to being a projective morphism. More precisely, a version of it states the following:
:If X ...
References
*
*.
*.
*
*.
*
formal GAGA
*
External links
*
*
*
formal GAGA
*
*
Theorems in algebraic geometry
{{abstract-algebra-stub