On the connected components of moduli spaces of Kisin modules
type: Item
instance of: scholarly article
title: On the connected components of moduli spaces of Kisin modules
zbMATH Open document ID: 1242.14043
author: Naoki Imai
published in: Journal of Algebra
publication date: 2012-05-23T00:00:00Z
reviewed by: Xiao Xiao
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 6037561
zbMATH Keywords: \(p\)-adic fields
zbMATH Keywords: moduli space
zbMATH Keywords: Kisin modules
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.09.031
OpenAlex ID: W2021933246
cites work: A modularity lifting theorem for weight two Hilbert modular forms
cites work: On the connected components of moduli spaces of finite flat models
cites work: Moduli of finite flat group schemes, and modularity
cites work: Schémas en groupes de type $(p,\ldots,p)$
DOI: 10.1016/J.JALGEBRA.2011.09.031
review text: Let \(K\) be a \(p\)-adic field, and let \(V_{\mathbb{F}}\) be a two-dimensional continuous representation of the absolute Galois group \(G_K\) over a finite field \(\mathbb{F}\) of characteristic \(p\). Let \(M_{\mathbb{F}}\) be a \(\phi\)-module corresponding to the Galois representation \(V_{\mathbb{F}}(-1)\), and \(\mathcal{GR}_{V_{\mathbb{F}}, 0}\) be the moduli space of Kisin modules in \(M_{\mathbb{F}}\) constructed in \textit{M. Kisin}'s paper [Ann. Math. (2) 170, No. 3, 1085--1180 (2009; Zbl 1201.14034)]. The author proves the followingNEWLINENEWLINETheorem. The non-ordinary locus of \(\mathcal{GR}_{V_{\mathbb{F}}, 0}^{\mathbf v}\), a closed subscheme of \(\mathcal{GR}_{V_{\mathbb{F}}, 0}\) determined by the condition that \(p\)-adic Hodge type is \({\mathbf v}=1\), is geometrically connected.NEWLINENEWLINEThe case when \(p>2\) was already proved by the author in a previous paper [Am. J. Math. 132, No. 5, 1189--1204 (2010; Zbl 1205.14025)]. This paper completes the proof of the theorem by proving the case when \(p=2\).
description: scientific article; zbMATH DE number 6037561