Jonah's question makes me wonder: What is with uniformization in algebraic/arithmetic geometry? E.g. this article by Faltings seems to be about that, the Shimura-Taniyama statement too, Mochizuki discusses a p-adic version of Fuchsian uniformization of hyperbolic curves. Do you know surveys or expositions of the theme? Or is 'uniformization' a mistaken concept in the context of arithmetic geometry (a remark in Faltings article sounds as if saying that)?
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Uniformization in algebraic/arithmetic geometry?Jonah's question makes me wonder: What is with uniformization in algebraic/arithmetic geometry? E.g. this article by Faltings seems to be about that, the Shimura-Taniyama statement too.
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