P-jets of finite algebras. I: $p$-divisible groups

Abstract

$p$-jets of finite flat maps of schemes are generally neither finite nor flat. However, for $p$-isogenies, and in particular for $p$-divisible groups, this pathology tends to disappear «in the limit". We illustrate this in the case of $G_m$, elliptic curves, and formal groups of finite height.