Deformations and liftings of finite, commutative group schemes | Zendy

Frans J. Oort | Zendy; David B. Mumford | Zendy

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Deformations and liftings of finite, commutative group schemes

Author(s) -

Frans J. Oort,

David B. Mumford

Publication year - 1968

Publication title -

inventiones mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.536

H-Index - 125

eISSN - 1432-1297

pISSN - 0020-9910

DOI - 10.1007/bf01389779

Subject(s) - mathematics , commutative property , pure mathematics , group (periodic table) , algebra over a field , organic chemistry , chemistry

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.

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