Note sur les p\'eriodes d'Iwasawa associ\'ees \`a un $\varphi$-module filtr\'e

TL;DR

This paper constructs a new sub-module for filtered φ-modules that encapsulates p-adic L-functions related to Galois representations, extending previous cases involving elliptic curves and modular forms.

Contribution

It introduces a generalized framework linking filtered φ-modules to p-adic L-functions within a novel sub-module structure.

Findings

Defines a sub- Z_p[[x]]-module for filtered φ-modules

Generalizes known cases from elliptic curves and modular forms

Connects p-adic L-functions to Galois representations in a new setting

Abstract

We associate to a filtered $\varphi$-module $D$ a sub-$Z_p[[x]]$-module of convergent series on the open unit disk in which the $p$-adic $L$-functions of the Galois representation associated to $D$ and the $Z_p$-cyclotomic extension live (if they exist). This generalizes the already known case where $D$ is associated to an elliptic curve or a modular form.