A local proof of the Breuil-M\'ezard conjecture in the scalar semi-simplification case

TL;DR

This paper presents a novel local proof of the Breuil-Mézard conjecture for certain reducible Galois representations with scalar semi-simplification, using Paškunas' formalism, advancing understanding in p-adic Hodge theory.

Contribution

It provides the first local proof of the conjecture in the scalar semi-simplification case, expanding the scope of known results in the field.

Findings

Proof of the Breuil-Mézard conjecture for reducible scalar semi-simplification cases

Application of Paškunas' formalism to this problem

Enhancement of techniques in p-adic Hodge theory

Abstract

We give a new local proof of the Breuil-M\'ezard conjecture in the case of a reducible representation of the absolute Galois group of $\mathbb{Q}_p$, $p>2$, that has scalar semi-simplification, via a formalism of Pa\v{s}k\=unas.