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 (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