On the freeness and projectiveness of Breuil-Kisin module

Abstract

In the work we have considered Breuil-Kisin module over the ring of witt vectors $W(\kappa )$ over the residue field $\kappa$ of characteristic $p$ and a finite flat ${\mathbb{Z}}_p$-algebra $R$. Then considered Breuil-Kisin modules $M$ over the ring $W(\kappa )$ and taking the action of $R$ on $W(\kappa )$, we get again a Breuil-Kisin module $M$ over the ring $R{\otimes }_{{\mathbb{Z}}_p}W(\kappa )$. We have studied freeness and projectiveness of this module.

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