I'm looking for Bruce W. Jordan's thesis: On the diophantine arithmetic of Shimura curves. Thesis, Harvard University, 1981. I could not find the pdf at the following site. https://www.math.harvard.edu/graduate/dissertations/ I could not find it in my university library either. Would it be possible to read it online? If it is not available on online, I will try to contact the author directly and ask.

Thank you in advance for your help.


1 Answer 1


This is Bruce Jordan. Essentially all the relevant parts of the thesis are in print: there is a Crelle paper on global points on Shimura curves and a Math. Ann. paper with Livne on local points. The thesis works out the canonical principal polarization on a QM abelian surface -- but this was stated (without proof) by Drinfeld and is surely due to Drinfeld. That computation is, I believe, also done by Voight in his book on quaternion algebras.

  • 1
    $\begingroup$ Thank you very much, Prof. Jordan! I am looking for references to the computation of "Shimura covering (maximal etale covering) of the Shimura curves", which is mentioned, for example, in Lemma 1.1 of Skorobogatov's "Shimura coverings of Shimura curves and the Manin obstruction". I looked at the papers you mentioned, but I couldn't find it. $\endgroup$
    – k.j.
    Mar 29 at 1:46
  • $\begingroup$ I understand the calculation. Thank you very much! $\endgroup$
    – k.j.
    Apr 14 at 6:51

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