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Dear mathoverflow community,

I'm looking for a translation (English, French or German) of Drinfeld's paper "Coverings of p-adic symmetric domains". If there is no translation out there, maybe someone knows other sources where the content of Drinfeld's paper is covered (in one of the three mentioned languages).

Thank you very much in advance.

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2 Answers 2

up vote 3 down vote accepted

The English translation of Drinfeld's paper is available here:

http://www.springerlink.com/content/j587364352k53717/

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Great! The original paper + the reference by Paul are exactly what I was looking for! Thanks to both of you! –  user5831 Oct 11 '11 at 17:53

In the following paper (in French), the authors consider the case of the $p$-adic upper half plane (the case of dimension $2$) and construct its coverings following Drinfeld.

Boutot, J.-F. and Carayol, H. Uniformisation $p$-adique des courbes de Shimura: les théorèmes de Čerednik et de Drinfelʹd. (French. English summary) [$p$-adic uniformization of Shimura curves: the theorems of Cherednik and Drinfelʹd] Courbes modulaires et courbes de Shimura (Orsay, 1987/1988). Astérisque No. 196-197 (1991), 7, 45–158 (1992).

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Thank you very much, this is a very good reference! I'm most interested in the relationship of coverings with Lubin-Tate theory and with the Serre-Tate theory on lifting abelian varieties. As far as I understand after a glance at your reference these things are contained but maybe a bit implicitly. I will have to think more to see if the results I'm looking for are in there (in a form I can understand ;) –  user5831 Oct 11 '11 at 17:39
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Cameron Franc has translated it into english: people.ucsc.edu/~cfranc/documents/bctranslation.pdf –  Thomas Riepe Oct 12 '11 at 5:19

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