In algebra, Schlessinger's theorem is a theorem in deformation theory introduced by Schlessinger (1968) that gives conditions for a functor of artinian local rings to be pro-representable, refining an earlier theorem of Grothendieck. == Definitions == Λ is a complete Noetherian local ring with residue field k, and C is the category of local Artinian Λ-algebras (meaning in particular that as modules over Λ they are finitely generated and Artinian) with residue field k.
In algebra, Schlessinger's theorem is a theorem in deformation theory introduced by Schlessinger (1968) that gives conditions for a functor of artinian local rings to be pro-representable, refining an earlier theorem of Grothendieck. == Definitions == Λ is a complete Noetherian local ring with residue field k, and C is the category of local Artinian Λ-algebras (meaning in particular that as modules over Λ they are finitely generated and Artinian) with residue field k.
Source: Wikipedia "Schlessinger's theorem" · CC BY-SA 4.0
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