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We construct integral models and special affinoids of suitable tubularneighborhoods of local Shimura varieties at depth-zero. We show that thereductions of the special affinoids over suitable tamely ramified extensionsare realized as parabolic Deligne-Lusztig varieties and explicitly compute partof the cohomology of local Shimura varieties at depth-zero. In the case ofgeneral linear groups, our constructions recover generalized semistable modelsof the Lubin-Tate spaces at depth-zero constructed by Yoshida.

On depth-zero integral models of local Shimura varieties