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Sep 16, 2020 at 15:25 comment added A.Skutin Is this argument valid for any other field which isn't algebraically closed but with zero characteristic?
Sep 16, 2020 at 14:02 comment added naf $\mathrm{Spec}(A)$ is obviously a curve which is unirational over $\mathbb{Q}$. It is also clear that the space of complex points of $\mathrm{Spec}(A)$ is contractible (in the analytic topology). There is only one curve over $\mathbb{Q}$ which has these two properties.
Sep 15, 2020 at 20:56 comment added Steven Landsburg @ulrich : what easy argument do you have in mind?
Sep 15, 2020 at 11:10 comment added A.Skutin I can only prove in case of algebraically closed field. Any hints to not closed field case?
Sep 15, 2020 at 10:48 comment added naf This is an easy exercise.
Sep 15, 2020 at 10:41 history edited YCor CC BY-SA 4.0
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Sep 15, 2020 at 10:17 history asked A.Skutin CC BY-SA 4.0