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9 votes
1 answer
543 views

Morphisms for good reduction are maps respecting filtration

Please see edits below! So, let $A,A'/K$ be abelian varieties where $K$ is a $p$-adic local field with residue field $k$. Suppose further that they have good reduction with models $\mathscr{A},\maths …
1 vote

Morphisms for good reduction are maps respecting filtration

The original question, as stated, has a negative answer. Namely, it is not true that the induced map $$\text{Hom}(A,A')\otimes\mathbb{Z}_p\to \text{Hom}_{F,V,\text{Fil}}(H^1_{\text{crys}}(\mathscr{A} …
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20 votes
0 answers
1k views

Is the Dieudonne module actually a cohomology group?

One often times thinks of the Dieudonne module $M(X)$ of a $p$-divisible group (say over $k$, a perfect characteristic $p$ field) as being some sort of cohomology theory $$M:\left\{p\text{- divisible …
9 votes
0 answers
428 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 …