A new method for overconvergence of {{\((\varphi ,\Gamma)\)}}-modules

TL;DR

This paper proves that all Laurent F-crystals over p-adic fields possess the property of overconvergence, expanding the understanding of their structure and behavior in p-adic Hodge theory.

Contribution

It establishes the overconvergence of all Laurent F-crystals over p-adic fields, a significant advancement in the theory of (φ,Γ)-modules.

Findings

All Laurent F-crystals over p-adic fields are overconvergent.

The result broadens the class of known overconvergent (φ,Γ)-modules.

Implications for p-adic Hodge theory and related areas.

Abstract

We show all Laurent $F$-crystals over $p$-adic fields are overconvergent.