Weight elimination in two dimensions when $p=2$

TL;DR

This paper proves a key part of Serre's conjecture related to mod 2 Galois representations for rank two unitary groups, extending previous results with new modifications.

Contribution

It establishes the weight elimination component of Serre's conjecture for mod 2 Galois representations, building upon and modifying prior foundational work.

Findings

Proves the weight elimination part of Serre's conjecture for p=2

Extends previous results with new modifications

Advances understanding of mod 2 Galois representations

Abstract

We prove the `weight elimination' part of the weight part of Serre's conjecture for mod 2 Galois representations for rank two unitary groups, by modifying the results in arXiv:1203.2552 and arXiv:1309.0527.