On depth-zero integral models of local Shimura varieties

Abstract

We specify explicit affinoids in depth-zero local Shimura varieties whose reductions are parabolic Deligne-Lusztig varieties, and construct explicit Jacquet-Langlands pairs of regular depth-zero supercuspidal representations in the cohomology of local Shimura varieties. Along the way, we develop the theory of integral moduli spaces of depth-zero level structures on local shtukas, especially at non-parahoric levels. As a consequence, we provide a direct construction of Yoshida's generalized semistable models of depth-zero Lubin-Tate spaces that were originally constructed as successive blowups.

60 pages; v3: added discussions on depth-zero integral models of Shimura varieties