Weight elimination in two dimensions when \(p=2\) (Q2107734)

The author proves 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 by \textit{T. Gee} et al. [J. Am. Math. Soc. 27, No. 2, 389--435 (2014; Zbl 1288.11045); Forum Math. Pi 3, Paper No. e2, 52 p. (2015; Zbl 1317.11045)]. The cited papers, in particular, prove similar results for mod \(p\) Galois representations for rank two unitary groups when \(p\) is odd prime. The author follows the same notations and ideas from these two papers.