The Emerton-Gee stacks for tame groups, II

Abstract: We construct the moduli stacks of potentially semistable $L$-parameters for tame $p$-adic groups. As an application, we give a recursive description of the irreducible components of the reduced Emerton-Gee stacks for classical groups. Our approach is grounded in a formalized framework whose axioms were previously confirmed in a separate preprint for both ramified and unramified unitary groups. When specialized to even unitary groups, we show the irreducible components of the reduced Emerton-Gee stacks are in natural bijection with parahoric Serre weights.