Questions tagged [dieudonne]

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2 votes
0 answers
143 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 ...
7 votes
0 answers
300 views

A citation from Dieudonné about existence, classification and construction

I am looking for an exact quote from Jean Dieudonné saying more or less that there are three kinds of important problems in mathematics: problems of existence, classification and construction. The ...
7 votes
0 answers
533 views

Dieudonne modules vs Dieudonne crystals reference/clarification

I've read a bit about Dieudonné modules, mainly from Fontaine's "Groupes p-divisibles sur les corps locaux" and Demazure's "Lectures on $p$-divisible groups". I am familiar with the main ...
14 votes
0 answers
524 views

Geometry underlying a comparison of Dieudonné theories

Maybe these hypotheses aren't necessary, but for me $\mathbb G$ will be a smooth formal group of dimension 1 and finite height over a perfect field $k$. There are several presentations of the ...
7 votes
1 answer
312 views

Dieudonné theory over non-perfect base fields

Is there a Dieudonné theory for $p$-divisible groups (or for finite flat group schemes of $p$-power order) over non-perfect base-fields?
3 votes
0 answers
231 views

Dieudonne modules and Cartier-Dieudonne module of a formal group

As far as I understand, there are Dieudonne modules defined through the homomorphisms to Witt covector scheme and Cartier-Dieudonne modules defined by curves. Am I right that the latter sometimes (for ...
9 votes
0 answers
401 views

Extension of Messing-Mazur-Oda to general groups

The following may be well-known (or obviously false), but I can't find a counterexample or a reference. Suppose that $k$ is some perfect field (one can assume algebraically closed, if that makes you ...
2 votes
0 answers
200 views

Two different definitions of $\sigma$-L-spaces in Kottwitz I and II

In his papers "Isocrystals with additional structure" I and II, Kottwitz defines the notion of $\sigma$-$L$-spaces. In the first one the situation is the following $k$ an algebraically closed field ...
2 votes
0 answers
469 views

$\sigma$-conjugate iff $p$-adically close

First some notations. Let $p$ be a prime, $k$ a perfect field of characteristic $p$, $W=W(k)$ the ring of Witt vectors over $k$, $\sigma : W \rightarrow W$ the Frobenius, $R$ a commutative $\mathbb{Z}...
4 votes
0 answers
452 views

Has anyone used this theorem of P. Cartier?

In "Groupes Algebriques et Groupes Formels", Conf. au coll. sur la theorie des groupes algebriques, Bruxelles 1962, P. Cartier proves the following in Section 9, Theoreme 1: (What follows is my ...