Wach models and overconvergence of étale (φ, Γ)-modules

2019/06/20 by Gao, Hui
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1906.09117

Abstract

A classical result of Cherbonnier and Colmez says that all étale (φ, Γ)-modules are overconvergent. In this paper, we give another proof of this fact when the base field K is a finite extension of \mathbb Q_p. Furthermore, we obtain an explicit ("uniform") lower bound for the overconvergence radius, which was previously not known. The method is similar to that in a previous joint paper with Tong Liu. Namely, we study Wach models (when K is unramified) in modulo pⁿ Galois representations, and use them to build an overconvergence basis.

Related

• Loose crystalline lifts and overconvergence of étale (φ, τ)-modules
• Overconvergence of étale (φ,Γ)-modules in families
• A new method for overconvergence of \((φ,Γ)\)-modules
• Locally analytic vectors and overconvergent (φ, τ)-modules
• Families of Galois representations and (φ, τ)-modules