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Results tagged with grothendieck-topology
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user 2874
18
votes
Accepted
Locally constant sheaves for the étale topology, lack of intuition about "étale-localness"
$Isom(F,G)$ is indeed an etale sheaf. If we take $F = \mathbb Z/n$ and $G = \mu_n$,
then $G$ is a sheaf of $F$-modules, and so evaluation at the global section $1$ gives an isomorphism of sheaves $Ho …
- 57.6k
20
votes
Are completions stalks under some Grothendieck topology?
You may want to look at the Artin approximation theorem. Roughly, it says (in the context of varieties, say) that any phenomenon you observe at the level of completions is already achieved etale loca …
- 57.6k
3
votes
Maps that admit local sections through each 'point' in the domain
I think that the property you want is the criterion for smoothness in terms of lifting maps over nilpotent thickenings. This is a way of expressing in algebraic terms the idea in manifold theory of h …
- 57.6k