We prove a version of the weight part of Serre’s conjecture for mod Galois representations attached to automorphic forms on rank 2 unitary groups which are nonsplit at . More precisely, let denote a CM extension of a totally real field such that every place of above is unramified and inert in , and let be a Galois parameter valued in the -group of a rank unitary group attached to . We assume that is semisimple and sufficiently generic at all places above . Using base change techniques and (a strengthened version of) the Taylor–Wiles–Kisin conditions, we prove that the set of Serre weights in which is modular agrees with the set of Serre weights predicted by Gee, Herzig and Savitt.
Karol Kozioł. Stefano Morra. "Serre weight conjectures for -adic unitary groups of rank ." Algebra Number Theory 16 (9) 2005 - 2097, 2022. https://doi.org/10.2140/ant.2022.16.2005