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Caruso, Xavier; David, Agnès; Mézard, Ariane

Stratified Kisin varieties and potentially Barsotti-Tate deformations. (Variétés de Kisin stratifiées et déformations potentiellement Barsotti-Tate.) (French. English summary) Zbl 1450.11050

J. Inst. Math. Jussieu 17, No. 5, 1019-1064 (2018).
Summary: Let \(F\) be a unramified finite extension of \(\mathbb{Q}_p\) and \(\overline{\rho}\) 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 \(\overline{\rho}\). We prove that this variety is a finite union of products of \(\mathbb{P}^1\). 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 \(\overline{\rho}\).

Cited in 1 Review
Cited in 4 Documents

MSC:

11F80 Galois representations
11S20 Galois theory
14L15 Group schemes

Keywords:

\(p\)-adic Hodge theory; Galois representations; deformations; Breuil-Kisin modules; Kisin variety
PDFBibTeX XMLCite
\textit{X. Caruso} et al., J. Inst. Math. Jussieu 17, No. 5, 1019--1064 (2018; Zbl 1450.11050)
Full Text: DOI arXiv

References:

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