Overconvergence Of Étale (φ, Γ)-modules In Families
In recent years, there has been growing interest in realizing the collection of
Langlands parameters in various settings as a moduli space with a geometric structure. In
particular, in the p-adic Langlands program, this space should come in two different forms of
moduli spaces of (φ, Γ)-modules: there is the "Banach" stack (also called the Emerton-Gee
stack), and the "analytic" stack. In this talk, I will present a proof of a recent conjecture
of Emerton, Gee and Hellmann concerning the overconvergence of étale (φ, Γ)-modules in
families, which gives a link between the two different moduli spaces.