Le cristal de Dieudonn\'e des sch\'emas en $\mathbb{F}$-vectoriels

Abstract

In this paper we describe the Dieudonn\'e crystal of a finite locally free group scheme with a vector action of a finite field $\mathbb{F}$. These $\mathbb{F}$-vector schemes appear when we consider torsion points of $p$-divisible modules. A particular class of $\mathbb{F}$-vector schemes has been classified by Raynaud in [Ray74], which allows us to determine the structure of torsion points of $p$-divisible modules, under certain conditions on the Lie algebra.