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Results tagged with crystalline-cohomology
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user 38867
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
$$M:\left\{p\text{- divisible …
- 777
9
votes
0
answers
428
views
Extension of Messing-Mazur-Oda to general groups
The following may be well-known (or obviously false), but I can't find a counterexample or a reference.
Suppose that $k$ is some perfect field (one can assume algebraically closed, if that makes you …
- 777
9
votes
1
answer
543
views
Morphisms for good reduction are maps respecting filtration
Please see edits below!
So, let $A,A'/K$ be abelian varieties where $K$ is a $p$-adic local field with residue field $k$. Suppose further that they have good reduction with models $\mathscr{A},\maths …
- 777
1
vote
Morphisms for good reduction are maps respecting filtration
The original question, as stated, has a negative answer. Namely, it is not true that the induced map
$$\text{Hom}(A,A')\otimes\mathbb{Z}_p\to \text{Hom}_{F,V,\text{Fil}}(H^1_{\text{crys}}(\mathscr{A} …