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

[摘要] A classical result of Cherbonnier and Colmez says that all kale (phi, r)-modules are overconvergent. In this paper, we give another proof of this fact when the base field K is a finite extension of 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 p(n) Galois representations, and use them to build an overconvergence basis. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Overconvergence;Wach modules