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Schottky Groups and Mumford Curves (Lecture Notes in Mathematics)
Schottky Groups and Mumford Curves (Lecture Notes in Mathematics)
Date: 21 June 2011, 01:37

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The idea of investigating the p-adic version of classical uniformizations of curves is due to John Tate who showed that an elliptic curve over a p-adic field K whose j-invariant has absolute value greater than 1 can be analytically uniformized. While Tate's original paper has never been published there are good accounts of his work available, see.
The generalization of the above result of Tate to curves of higher genus has been given by David Mumford in 1972 in a work called "Analytic construction of degenerating curves over complete local rings".

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