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

## TL;DR

This paper explores the Dieudonné crystal associated with finite locally free group schemes equipped with a finite field vector action, crucial for understanding torsion points of p-divisible modules.

## Contribution

It describes the Dieudonné crystal structure for -vector schemes, extending Raynaud's classification to analyze torsion points of p-divisible modules under specific Lie algebra conditions.

## Key findings

- Characterization of Dieudonné crystals for -vector schemes
- Extension of Raynaud's classification to new cases
- Insights into the structure of torsion points of p-divisible modules

## 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.