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9
votes
Accepted
On a quasi-separated assumption in a lemma for the homotopy exact sequence of the etale fund...
This is more a comment than an answer: a few years back, in 2011, while working with some friends on SGA1, we also found out that we could not prove this statement without the hypothesis that $X$ is q …
4
votes
Does a curve over a number field have a finite etale cover of given degree
This is not a complete answer, but I am trying to translate your issue in something more tractable.
If you assume there exists a rational point $x$, then the image of the corresponding section $s=s_ …