On the quaternionic Serre weights

TL;DR

This paper determines the set of quaternionic Serre weights for generic two-dimensional mod p Galois representations over unramified extensions of Qp, advancing understanding in the area of modular forms and Galois representations.

Contribution

It explicitly characterizes quaternionic Serre weights for generic two-dimensional mod p Galois representations over unramified extensions of Qp.

Findings

Identifies the set of quaternionic Serre weights for the specified Galois representations.

Provides a classification that applies to generic cases over unramified extensions.

Enhances the understanding of the relationship between Galois representations and modular forms.

Abstract

We determine the set of quaternionic Serre weights for generic two-dimensional mod $p$ representation of $\operatorname{Gal}(\overline{\mathbb Q}_p / K)$, where $K$ is a finite unramified extension of $\mathbb{Q}_p$.