The plectic conjecture over local fields

Abstract Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekovář–Scholl’s plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after restricting to a decomposition group. Along the way, we prove a 𝑝-adic uniformization theorem for the basic locus of abelian type Shimura varieties at hyperspecial level, which is of independent interest.