| Résume | We consider a generalisation of Serre's conjecture for irreducible, conjugate self-dual Galois representations $\rho : G_F \rightarrow GL_3(\overline{\mathbb{F}_p})$, where $F$ is a CM field in which $p$ splits completely. We previously gave a conjecture for the possible Serre weights of $\rho$. If $\rho$ is locally irreducible at $p$ and modular of a (very) generic Serre weight, we show that the set of generic Serre weights of $\rho$ coincides precisely with the conjectural set. This is joint work with Matthew Emerton and Toby Gee. |
