Properties of Breuil-Kisin modules inherited by $p$-divisible groups

Abstract

In this paper, by assuming a faithful action of a finite flat ${\mathbb{Z}}_p$-algebra $\mathcal{R}$ on a $p$-divisible group $\mathcal{G}$ defined over the ring of $p$-adic integers ${\mathcal{O}}_K$, we construct a category of new Breuil-Kisin module $\mathfrak{M}$ defined over the ring $\mathfrak{S}:=W(\kappa )[[u]]$ and study the freeness and projectiveness properties of such a module.

arXiv comment10 pages, we studied the properties of Breuil-Kisin modules and any comments regarding the work are mostly welcome