Vol. 298, No. 2, 2019

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Semistable deformation rings in even Hodge–Tate weights

Lucio Guerberoff and Chol Park

Vol. 298 (2019), No. 2, 299–374
Abstract

Let p be a prime number and r a positive even integer less than p 1. In this paper, we find a Galois stable lattice in each two-dimensional semistable noncrystalline representation of Gp with Hodge–Tate weights (0,r) by constructing the corresponding strongly divisible module. We also compute the Breuil modules corresponding to the mod p reductions of these strongly divisible modules, and determine the semisimplification of the mod p reduction of the original representations. We use these results to construct the irreducible components of the semistable deformation rings in Hodge–Tate weights (0,r) of the absolutely irreducible residual representations of Gp.

Keywords
semistable representations, strongly divisible modules, Breuil modules, semistable deformation rings
Mathematical Subject Classification 2010
Primary: 11F80
Milestones
Received: 30 March 2017
Revised: 30 January 2018
Accepted: 12 May 2018
Published: 8 March 2019
Authors
Lucio Guerberoff
Department of Mathematics
University College London
London
United Kingdom
Chol Park
School of Mathematics
Korea Institute for Advanced Study
Seoul
South Korea