Questions tagged [p-divisible-group-schemes]
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13 questions
2 votes
0 answers
95 views
Quasi-isogeny corresponding to the image of the Frobenius in the Dieudonné module of a $p$-divisible group
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 $\...
- 821
2 votes
0 answers
194 views
Explicit description of the crystal associated to the universal object on a Lubin-Tate space
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-...
- 29
1 vote
0 answers
111 views
Description of a finite group scheme $G_{1,1}[p]$
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 $D(k)/D(k)(F-V)$ ...
- 141
1 vote
0 answers
140 views
Descent of isogenies between p-divisible groups
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 ...
- 83
5 votes
0 answers
250 views
When is the image of $\operatorname{Gal}(\bar K/K)$ open in $\operatorname{Aut}(V)$, where $V$ is the vector space coming from a $p$-adic Tate module?
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 $...
- 441
2 votes
0 answers
251 views
Computing the Dieudonné module of $\mu_p$ from Fontaine's Witt Covector
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 ...
- 389
4 votes
0 answers
109 views
Conditions for a $p$-divisible group to be represented by a formal Lie group
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 ...
- 51
6 votes
1 answer
342 views
Generating the coordinate ring of the Lubin-Tate formal group
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 ...
- 2,277
4 votes
1 answer
351 views
Relation between rational Tate module and universal cover of a p-divisible group
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 ...
- 1,123
2 votes
0 answers
149 views
Deformation of Display on Zink's paper
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, ...
- 397
4 votes
1 answer
226 views
What is the reason behind the name 3n-display?
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 ...
- 1,123
0 votes
0 answers
389 views
Any finite flat commutative group scheme of $p$-power order is etale if $p$ is invertible on the base
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 ...
- 3,914
1 vote
0 answers
302 views
Deformation of $p$-divisible group
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 $G_0$ ...
- 397