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