What are some geometric applications of integral p-adic Hodge theory (as opposed to rational p-adic Hodge theory)? I am aware of certain applications to the question of nice reductions of varieties (e.g. [this][1] or [this][2]). It appears that [this question][3] is not a duplicate since the paper of Berthelot et al mentioned there uses rational p-adic Hodge theory. [1]: https://arxiv.org/abs/1003.2905 [2]: https://arxiv.org/abs/1802.07396 [3]: https://mathoverflow.net/questions/191254/applications-of-p-adic-hodge-theory