Over the winter break I finished translating the second chapter of Boutot-Carayol’s long Asterisque paper “Uniformisation -adique des courbes de Shimura: les theoremes de Cerednik et de Drinfeld” into english. Their paper explains Drinfeld’s proof of Cerednik’s p-adic uniformization theorem for certain Shimura curves, which relies on a moduli interpretation for the p-adic upper half plane in terms of certain formal groups with extra structure. Originally Cerednik proved his theorem using some brute force techniques, and Drinfeld later gave the more conceptual moduli interpretation. In the coming months I intend to translate the rest of the document as well. For now I’m happy enough with the second chapter to link to it here.

## January 18, 2010

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