Sur les repr\'esentations absolument na\"ives et leur module de Wach

TL;DR

This paper constructs Wach modules for a class of semi-stable Galois representations satisfying Griffiths transversality, extending previous crystalline cases, and applies this to describe representations factoring through the Tate curve extension.

Contribution

It introduces a new construction of Wach modules for semi-stable representations with Griffiths transversality, broadening the scope beyond crystalline cases.

Findings

Wach modules constructed for semi-stable representations with Griffiths transversality

Extension of Wach and Berger's methods to semi-stable case

Application to representations factoring through the Tate curve extension

Abstract

We construct a Wach module for the absolutely semi-stable representations the filtered $(\varphi, N)$-module of which satisfies the Griffiths transversality, which happens in particular for ordinary representations. This construction extends the ones of Wach and Berger for the absolutely crystalline case. We use it in particular to describe semi-stable representations which factor through the Tate curve extension.