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Group Schemes over artinian rings and Applications

Ioan Berbec — 2009

Annales de l’institut Fourier

Let n be a positive integer and A a complete characteristic zero discrete valuation ring with maximal ideal 𝔪 , absolute ramification index e < p - 1 and perfect residue field k of characteristic p > 2 . In this paper we classify smooth finite dimensional formal p - groups over A n = A / 𝔪 n A , groups on which the “multiplication by p ” morphism is faithfully flat, in particular p -divisible groups. As applications, we prove that p -divisible groups over k , and the morphisms between them, lift canonically to A / p A , and we study liftings...

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