A note on multivariable $$(\varphi ,\Gamma )$$ ( φ , Γ ) -modules

On Families of (φ,Γ)-modules

We prove that every family of (overconvergent) étale (φ,Γ)-modules over a reduced affinoid algebra can be locally converted to a family of p-adic representations uniquely.

6. Φ-Γ-modules and Galois cohomology

A method to solve it for G = GK (K is a local field) is to use Fontaine’s theory of ΦΓ-modules and pass to a simpler Galois representation, paying the price of enlarging Zp to the ring of integers of a two-dimensional local field. In doing this we have to replace linear with semi-linear actions. In this paper we give an overview of the applications of such techniques in different situations. We...

New Methods for (φ,γ)-modules

Let p be a prime number. The subject of p-adic Hodge theory concerns the interplay between different objects arising from the cohomology of algebraic varieties over p-adic fields. A good introduction to the subject can be found in the notes of Brinon and Conrad [3]; here, we limit discussion to two proofs which we feel are simpler than their counterparts in the literature. Our original motivati...

A p - ADIC FAMILY OF DIHEDRAL ( φ , Γ ) - MODULES by

— The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (φ,Γ)-modules by writing down explicit matrices for φ and for the action of Γ, and finally to determine which of these are trianguline. Résumé (Une famille p-adique de (φ,Γ)-modules diédraux). — L’objet de cet article est de construire expl...

A Note on Finsler Modules