Variétés de Kisin stratifiées et déformations potentiellement Barsotti-Tate

Abstract : Let F be a unramified finite extension of Qp and rhobar 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 rhobar. We prove that this variety is a finite union of products of P^1. Moreover, it appears as an explicit closed subvariety of P^1^[F:\Qp]. 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 rhobar.
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Xavier Caruso, Agnès David, Ariane Mézard. Variétés de Kisin stratifiées et déformations potentiellement Barsotti-Tate. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2017, 46 p. ⟨10.1017/S1474748016000232⟩. ⟨hal-01162557v2⟩



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