Quasi-semi-stable representations

TL;DR

This paper introduces quasi-semi-stable p-adic torsion representations of G_ _infty, providing an explicit linear algebraic description, and aims to deepen understanding of quotients of lattices in crystalline and semi-stable Galois representations.

Contribution

It defines a new class of p-adic torsion representations called quasi-semi-stable and describes their structure via linear algebra objects, advancing the study of Galois representations.

Findings

Quasi-semi-stable representations are explicitly characterized.

The paper establishes a linear algebraic framework for these representations.

Results serve as a foundation for understanding quotients in crystalline and semi-stable cases.

Abstract

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of p-adic torsion representations of G_\infty, named quasi-semi-stable. We prove that these representations are "explicitly" described by a certain category of linear algebra objects. The results of this note should be consider as a first step in the understanding of the structure of quotients of two lattices in a crystalline (resp. semi-stable) Galois representation.