#### Vol. 9, No. 8, 2015

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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 $\left(\phi ,Ĝ\right)$-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
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