p-Divisible Groups

J. T. Tate

A chapter in Proceedings of a Conference on Local Fields, 1967, pp 158-183 from Springer

Abstract: Abstract After a brief review of facts about finite locally free commutative group schemes in § 1, we define p-divisible groups in § 2, and discuss their relation to formal Lie groups. The § 3 contains some theorems about the action of Gal (K̄/K) on the completion C of the algebraic closure of a local field K of characteristic 0. In § 4 these theorems are applied to obtain information about the Galois module of points of finite order on a p-divisible group G defined over the ring of integers R in such a field K, and to prove that G is determined by that Galois module, or, what is the same, by its generic fiber G ×R K.

Keywords: Exact Sequence; Group Scheme; Residue Field; Finite Extension; General Fiber (search for similar items in EconPapers)
Date: 1967
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DOI: 10.1007/978-3-642-87942-5_12

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