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Results tagged with grothendieck-topology
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user 36285
7
votes
1
answer
462
views
Needless axiom for Grothendieck topologies?
Hi,
The first axiom for a Grothendieck (pre)topology on a category $C$ says that for every object $X\in C$, the family consisting of just the identity $1_X : X\to X$ should be a covering family.
Why …
- 2,842
20
votes
1
answer
3k
views
Crystalline cohomology via the syntomic site
Hello,
Let $k$ be a field of characteristic $p > 0$, and let $Y$ be a $k$-scheme. Consider the
sites $Y_{syn}$ and $(Y/W_n)_{cris}$ (where $W_n$ are the Witt vectors of $k$ of length $n$), of $Y$ wit …
- 2,842
25
votes
Accepted
Crystalline cohomology via the syntomic site
A sketch of the proof is as follows:
Consider the site $Y_{syn-cris}$ where the objects are the same as in $Y_{cris}$ but the
covering families are surjective syntomic families. Then there are maps o …
- 2,842
5
votes
0
answers
349
views
cech cohomology in topos
Hi,
The following result seems to be well known, but I can't come up with a proof.
Suppose that $C$ is a topos and that $F\to G$ is an effective epimorphism in $C$. If $P$ is
any abelian sheaf on $C …
- 2,842