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Deformations and liftings of finite, commutative group schemes

1968; Springer Science+Business Media; Volume: 5; Issue: 4 Linguagem: Inglês

10.1007/bf01389779

1432-1297

Frans J. Oort, David B. Mumford,

Advanced Topics in Algebra

The answers to (A) and to the weaker question (B) are negative in general. However if in (B) moreover is given that N o is a commutative finite group scheme, the answer is affirmative; it is the aim of this paper to give a proof of this fact via deformation theory of finite group schemes in characteristic p > 0. As a byproduct we obtain a proof for the fact that any finite, local group scheme can be embedded into a formal Lie group with coefficients in the same field, on the same number of parameters.