On depth-zero integral models of local Shimura varieties

We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as parabolic Deligne-Lusztig varieties and explicitly compute part of the cohomology of local Shimura varieties at depth-zero. In the case of general linear groups, our constructions recover generalized semistable models of the Lubin-Tate spaces at depth-zero constructed by Yoshida.