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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

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

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

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  • $\begingroup$ Great! The original paper + the reference by Paul are exactly what I was looking for! Thanks to both of you! $\endgroup$
    – user5831
    Commented Oct 11, 2011 at 17:53
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    $\begingroup$ I couldn't make the link in the answer work. Possibly it is now broken. However link.springer.com/article/10.1007%2FBF01077936 seems to work for me. $\endgroup$
    – Simon Wadsley
    Commented Jul 20, 2021 at 13:30
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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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  • $\begingroup$ 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 ;) $\endgroup$
    – user5831
    Commented Oct 11, 2011 at 17:39
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    $\begingroup$ Cameron Franc has translated it into english: people.ucsc.edu/~cfranc/documents/bctranslation.pdf $\endgroup$
    – Thomas Riepe
    Commented Oct 12, 2011 at 5:19
  • $\begingroup$ @ThomasRiepe that link is no longer working. A currently working link is www-personal.umich.edu/~francc/files/bctranslation.pdf (even though Cameron is no longer at Michigan). I found that link in a comment on the page mathoverflow.net/questions/215017/…. $\endgroup$
    – KConrad
    Commented May 27, 2021 at 18:24

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