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Results tagged with fundamental-group
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user 4790
33
votes
Accepted
Profinite groups as étale fundamental groups
[Edit:] The answer should be positive, that is, every profinite group appears as the fundamental group of a scheme. Here is a sketch of proof.
First of all, I claim that for any finite group $G$ ther …
- 27k
9
votes
Accepted
locally constant constructible sheaves and finite etale coverings
Consider your functor from étale coverings to locally constant constructible sheaves. It is fully faithful, by Yoneda's lemma. The fact that it is essentially surjective follows from descent theory. I …
- 27k
1
vote
Finite vector bundles over punctured affine spaces
By Nori's theorem, the existence of non-trivial finite vector bundles on a reduced connected scheme $X$ of finite type over a perfect field $k$ with a rational point is equivalent to the fact that for …
- 27k