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Questions tagged [p-divisible-group-schemes]

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14 questions
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1 vote
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Let $G$ be a simple $p$-divisible group over $\mathbb{Z}_p$ (arising from a formal group over $\mathbb{Z}_p$, so connected), and let $V := T_p(G)\otimes_{\mathbb Z_p}\mathbb Q_p$ be its Tate module. ...
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2 votes
0 answers
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Let $X$ be a $p$-divisible group over a perfect field $k$ of characteristic $p>0$. Let $M(X)$ be the covariant Dieudonné module of $X$. Thus, $M(X)$ is a finite free $W(k)$-module equipped with a $\...
Suzet's user avatar
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Let $X:=\mathrm{LT}_h$ be the Lubin-Tate space of the (unique) formal group law of height $h$ over $k:=\overline{\mathbb{F}}_p$. The adic generic fiber $X_{\eta}=\mathrm{LT}_{h,\eta}$ is then a rigid-...
XYZhou's user avatar
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Ler $k$ be a perfect field of characterisic $p$. Let $G=G_{1,1}$ denote the $p$-divisible group of a supersingular elliptic curve over $k$, its Cartier-Dieudonne module is given by $D(k)/D(k)(F-V)$ ...
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Let $\mathcal{G}$ be a $p$-divisible group over $K$, which is a finite extension of $\mathbb{Q}_p$. Let $\rho: \text{Gal}(\bar{K}/K)\rightarrow \text{GL}(T_p\mathcal{G})$ be the associated Galois ...
Razumikhin's user avatar
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4 votes
0 answers
251 views

Let $K$ be a finite extension of $\mathbb{Q}_p$ with ring of integers $A$. Let $F$ be a $p$-divisible group and $T$ be the Tate module. Consider the vector space $V=T \otimes_{\mathbb{Q}_p} C$, where $...
Learner's user avatar
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3 votes
0 answers
269 views

In Groupes $p$-divisibles sur les corps locaux, Fontaine introduced a uniform construction of Dieudonné modules through the definition of the Witt covector. Consider a perfect field $k$ of ...
HJK's user avatar
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Let $S$ be a scheme where $p$ is locally nilpotent and let $G$ be a $p$-divisible group over $S$. Is connectedness of $G$ equivalent to $G[p] := \ker(p : G \to G) \to S$ radicial (universally ...
kiwi's user avatar
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6 votes
1 answer
397 views

Let $K$ be a $p$-adic local field with uniformizer $\pi \in \mathcal{O}_{K}$ and residue field $k = \mathcal{O}_{K}/\pi$. Let $G$ be a Lubin-Tate formal $\mathcal{O}_{K}$-module and $G_{0}$ its ...
Piotr Pstrągowski's user avatar
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4 votes
1 answer
360 views

We can associate two $\mathbb Q_p$ vector spaces to a $p$-divisible group, and I'm a little confused about the relation between these two groups. First of all, I think part of my problem is that when ...
ali's user avatar
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2 votes
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163 views

I am going to compute some intersection numbers on certain RZ spaces and therefore need to fully understand the deformation of $p$-divisible groups. This can be understood as deformation of displays, ...
Qirui Li's user avatar
  • 397
4 votes
1 answer
228 views

In the paper "The display of a formal $p$-divisible group" Zink defines some objects and calls them $3n$-display. A $3n$-display over $R$ is a quadruple $P$, $Q$, $F$, $F^1$ such that $P$ is ...
ali's user avatar
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0 answers
396 views

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 ...
user267839's user avatar
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1 vote
0 answers
306 views

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 $G_0$ ...
Qirui Li's user avatar
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