G-valued crystalline representations with minuscule p-adic Hodge type

Levin, Brandon

doi:10.2140/ant.2015.9.17

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$G$-valued crystalline representations with minuscule $p$-adic Hodge type

Brandon Levin

Vol. 9 (2015), No. 8, 1741–1792

DOI: 10.2140/ant.2015.9.17

Abstract

We study $G$ -valued semistable Galois deformation rings, where $G$ is a reductive group. We develop a theory of Kisin modules with $G$ -structure and use this to identify the connected components of crystalline deformation rings of minuscule $p$ -adic Hodge type with the connected components of moduli of “finite flat models with $G$ -structure”. The main ingredients are a construction in integral $p$ -adic Hodge theory using Liu’s theory of $(φ, Ĝ)$ -modules and the local models constructed by Pappas and Zhu.

Keywords

Galois representation, $p$-adic Hodge theory, finite flat group scheme, local model

Mathematical Subject Classification 2010

Primary: 11S20

Secondary: 14L15, 14F30

Milestones

Received: 4 April 2014

Revised: 1 June 2015

Accepted: 15 July 2015

Published: 29 October 2015

Authors

Brandon Levin
Department of Mathematics University of Chicago 5734 S. University Avenue, Room 208C Chicago, 60637 United States

Vol. 9, No. 8, 2015