This question is immediately related to Discriminant ideal in a member of Barsotti-Tate Group dealing with Barsotti–Tate groups and here I would like to clarify a proof presented by Anonymous in the comments from linked thread which I do not completely understand. Although meanwhile I found anoth...

To try to understand the deformation of $p$-divisible group more explicit, I am thinking given a connected $p$-divisible group $G_0$ on $\overline{\mathbb{F}_q}$, Choose a deformation $G$ of $G_0$ over $W(\overline{\mathbb{F}_q})/p^2$, then it determines a filtration in Dieudonné module (maybe up...

I am working on a problem in sequences. The theorem I am trying to prove requires the following implication. But I am not sure how to prove this. Kindly share your thoughts. Let $(y_n)$ be a sequence which is not Cauchy but satisfies $\lim_{n\to\infty} d(y_n,y_{n+1})=0$. Then there exists an $\ep...