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?

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