We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a \(\delta \)-structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible groups.

中文翻译：

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规范升降和$$ \ delta $$δ结构

我们将普通阿贝尔变种规范提升的Serre-Tate理论扩展到通过p- adic形式方案S参数化的任意非极化普通阿贝变种族。我们证明规范提升是W（S）的唯一提升，它在Joyal，Buium和Bousfield的意义上允许\（\ delta \）-结构。我们证明了普通p-基和p-可整基族的相似陈述。