VARIÉTÉS DE KISIN STRATIFIÉES ET DÉFORMATIONS POTENTIELLEMENT BARSOTTI-TATE

Xavier Caruso, Agnès David, Ariane Mézard
2016 Journal of the Institute of Mathematics of Jussieu  
Let$F$be a unramified finite extension of$\mathbb{Q}_{p}$and$\overline{\unicode[STIX]{x1D70C}}$be an irreducible mod$p$two-dimensional representation of the absolute Galois group of$F$. The aim of this article is the explicit computation of the Kisin variety parameterizing the Breuil–Kisin modules associated to certain families of potentially Barsotti–Tate deformations of$\overline{\unicode[STIX]{x1D70C}}$. We prove that this variety is a finite union of products of$\mathbb{P}^{1}$. Moreover,
more » ... }^{1}$. Moreover, it appears as an explicit closed connected subvariety of$(\mathbb{P}^{1})^{[F:\mathbb{Q}_{p}]}$. We define a stratification of the Kisin variety by locally closed subschemes and explain how the Kisin variety equipped with its stratification may help in determining the ring of Barsotti–Tate deformations of $\overline{\unicode[STIX]{x1D70C}}$.
doi:10.1017/s1474748016000232 fatcat:poewjmk4krdldlrucrzlnafloy