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Results tagged with grothendieck-topology
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user 4790
34
votes
Accepted
In what sense is the étale topology equivalent to the Euclidean topology?
Saying that the étale topology is equivalent to the euclidean topology is vastly overstating the case. For example, if you compute the cohomology of a complex algebraic variety with coefficients in $\ …
- 27k
6
votes
Zariski sheaves lifted to etale topology
I don't think so. Let $X$ be $\mathbb A^1_{\mathbb C}$ with two points glued together, and let $Y$ be the standard double étale cover, obtained by identifying two copies of $\mathbb A^1$. I claim that …
- 27k
4
votes
Accepted
Can Inequivalent Topologies Have Same Sheaves/Cohomology?
I would think so.
Two pretopologies are equivalent when they generate the same topology, that is, when the have the same sieves. If $A$ is an object of $C$, a sieve on $A$ is a subfunctor of the fun …
- 27k
3
votes
Accepted
fppf-extension of algebraic groups is an algebraic group
Here is a possible road to a solution (I am fairly sure that Milne had something more elementary in mind). Algebraic spaces satisfy fppf descent; hence $G$ is a group object is in the category of alge …
- 27k