Potential automorphy of $${\text {GSpin}}_{2n+1}$$-valued Galois representations

Mod $p$ local-global compatibility for $\mathrm{GSp}_4(\mathbb{Q}_p)$ in the ordinary case

“…In §4.4, we assume that ρ is a local component of a Galois representation r : G F → GSp 4 (F) modular with respect to G satisfying several assumptions (A1)-(A5) including standard Taylor-Wiles type assumptions, but also an unramifiedness away from p assumption that is made mainly for simplicity. We also show the existence of such F and r for given ρ by following [EG14] and using the main result from [PT21]. See Corollary 4.4.5 for the precise statement.…”

“…is only used to apply the main result of [KS]. Instead, we use [Mok14, Theorem 3.5] to remove the Steinberg condition (see the paragraph after Theorem 1.3 of [PT21]). As already mentioned in the Remark 4.4 of loc.…”