F_p-repr\'esentations semi-stables

TL;DR

This paper introduces the concept of pylonets to study torsion semi-stable Galois representations via Breuil modules, establishing abelian subcategories and explicit computational tools.

Contribution

It defines pylonets within Breuil modules categories and constructs abelian subcategories, enhancing the understanding and computability of torsion semi-stable representations.

Findings

Categories of Breuil modules form pylonets

Established abelian subcategories with desirable properties

Provided explicit methods for computations in Galois representations

Abstract

Torsion semi-stable representations can be constructed and studied using Breuil modules. In this paper, we define the notion of pylonet and prove that some categories of Breuil modules naturally define pylonets. As a consequence, we are able to define full subcategories of Breuil's categories with very nice properties (in particular, they are abelian). In a second part of this work, we try to make very explicit some abstract constructions coming from the general theory of pylonets (developped earlier in the paper). These explicitations should be very useful to make computations with torsion semi-stable Galois representations.