On depth-zero integral models of local Shimura varieties

TL;DR

This paper constructs integral models of depth-zero local Shimura varieties, showing their reductions relate to Deligne-Lusztig varieties and computing parts of their e9tale cohomology, extending known models for GL groups.

Contribution

It introduces new integral models for depth-zero local Shimura varieties and explicitly computes their e9tale cohomology, connecting to Deligne-Lusztig varieties and generalizing Lubin-Tate models.

Findings

Reductions of models are parabolic Deligne-Lusztig varieties.

Part of the e9tale cohomology is explicitly computed.

Recovers known models for GL groups at depth-zero.

Abstract

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 middle $\ell$-adic \'{e}tale cohomology of local Shimura varieties at depth-zero. In the case of general linear groups, our construction recovers generalized semistable models of Lubin-Tate spaces at depth-zero constructed by Yoshida.