The overconvergence of multivariable $(\ddot{I}{†}_q,{\mathcal{O}}_K^{\times })$-modules at the perfectoid level

Changjiang Du

Let $K$ be a finite unramified extension of ${\mathbb{Q}}_p$, and $E$ a finite extension of $K$ with ring of integers ${\mathcal{O}}_E$. We define the overconvergence of multivariable…