What are some geometric applications of integral p-adic Hodge theory (as opposed to rational p-adic Hodge theory)? Answers which understand Hodge theory as the study of Galois stable $\mathbb{Z}_p$-lattices are OK but I am more interested in applications of comparison theorems (like the one recently established by Bhatt--Morrow--Scholze).
I am aware of certain applications to the question of nice reductions of varieties (e.g. this or this).
It appears that this question is not a duplicate since the paper of Berthelot et al mentioned there uses rational p-adic Hodge theory.