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### Universal covering space of a Zariski open subset of projective space

Let $U$ be a Zariski open subset of $\mathbb P^n_{\mathbb C}$. Assume $U$ is the complement of some divisors.
Have the possible universal covering spaces of $U$ been classified?
Do we know when the ...

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### Ramification: Riemann surfaces vs Number fields

I am trying to understand the connection between Riemann surfaces and number fields. I am wondering if there an inconsistency in the definition of ramification in terms of Riemann surfaces vs number ...