Deformations of Prismatic Higher $(G,\mu )$-Displays over Quasi-Syntomic Rings

We prove a deformation theorem for prismatic higher $(G,\mu )$-displays over quasi-syntomic rings. As an application, we extend the classification of $p$-divisible groups via prismatic Dieudonné modules to a class of rings, properly containing quasi-syntomic rings. Finally, we relate the stack of prismatic higher $(G,\mu )$-displays to integral local Shimura varieties.