Geometric properties of the analytic Emerton-Gee stack

Abstract

The analytic Emerton-Gee stack is a rigid analytic moduli stack of $(φ,Γ)$-modules over the Robba ring, and is expected to play a fundamental role in the categorical $p$-adic local Langlands correspondence for locally analytic representations. In this paper, we establish the fundamental geometric properties of the analytic Emerton-Gee stack: it is a rigid analytic Artin stack, normal, a local complete intersection, and equidimensional of the expected dimension. As an application, our normality result removes the reducedness hypothesis in the paper of Le, Strauch, and Wang, thereby yielding an unconditional proof of the conjecture on the global sections of the analytic Emerton-Gee stack formulated by Emerton, Gee, and Hellmann.