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Timeline for Existence of local sections

Current License: CC BY-SA 3.0

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Apr 6, 2014 at 18:00 comment added user49221 Thanks, I am aware of this case. However, it is not so weird to have degrees of the sections going off to $\infty$. For example, one might construct sections using Frobenius in some way, so the degree could grow like the residue characteristic. (In fact, this is how the question arose for me.)
Apr 6, 2014 at 17:36 history answered Piotr Achinger CC BY-SA 3.0