Semistable deformation rings in even Hodge–Tate weights

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 GQp 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 GQp.