Dear community, In light of the recent work of DeBacker/Reeder on the depth zero local Langlands correspondence, I was wondering if there is an attempt to "geometrize" the depth zero local Langlands correspondence. In particular, in Teruyoshi Yoshida's thesis, one can see a glimpse of this for , 略 Sincerely, Moshe Adrian edited May 7 2011 at 3:13
Teruyoshi Yoshida responded to my question by e-mail and he is ok with my posting his response on mathoverflow : "Dear Moshe, thanks for your interest - yes it would be very interesting to do this with more general Rapoport-Zink spaces, but i) I haven't been successful in finding an intrinsic moduli interpretation of my model for tame Lubin-Tate space, hence the difficulty in generalizing to other groups ii) the so-called Drinfeld level structures do not seem to give nice integral models for the Rapoport-Zink spaces with deeper levels. In spite of these obstacles in arithmetic-geometry, it would be interesting to investigate the cohomology for other RZ spaces (there are works by Ito-Mieda, Shin, Strauch etc). Feel free to quote my email in mathoverflow.
