Induction and restriction of (\phi,\Gamma)-modules

TL;DR

This paper develops a variant of (e,) -modules theory for non-archimedean local fields, enabling explicit computation of induction and restriction functors when changing the base field, and revisits overconvergence results in this context.

Contribution

It introduces a new framework replacing Lubin-Tate towers with maximal abelian extensions for (e,)-modules, facilitating functor computations across different fields.

Findings

Computed induction and restriction functors for (e,)-modules.

Provided a self-contained proof of overconvergence in the new setting.

Extended the theory to include maximal abelian extensions.

Abstract

Let L be a non-archimedean local field of characteristic 0. We present a variant of the theory of (\phi,\Gamma)-modules associated with Lubin-Tate groups, developed by Kisin and Ren [Ki-Re], in which we replace the Lubin-Tate tower by the maximal abelian extension \Gamma = Gal(L^ab/L). This variation allows us to compute the functors of induction and restriction for (\phi,\Gamma)-modules, when the ground field L changes. We also give a self-contained account of the Cherbonnier-Colmez theorem on overconvergence in our setting.