Let be a completed algebraic closure of , and let be a p-divisible group. The Tate module of sits in a Hodge-Tate sequence
According to a recent theorem of Scholze-Weinstein, the map induces an equivalence of categories from the category of p-divisible groups over to the category of pairs where is a free finite rank -module and is a -sub-vector-space.
So here’s the puzzle. Let be an abelian variety over ; this has an analogous Hodge-Tate sequence, and the pair gives rise to a p-divisible group . What is the relationship between and when has bad reduction?