Galois Lattices and Strongly Divisible Lattices in the Unipotent Case

Let p be a prime. We prove that there is an anti-equivalence between the category of unipotent strongly divisible lattices of weight p-1 and the category of Galois stable Z_p lattices in unipotent semi-stable representations with Hodge-Tate weights in {0, ..., p-1}. This completes the last remaining piece of Breuil's Conjecture(Conjecture 2.2.6 in [Bre02]).