We prove that for forms of which are compact at infinity and split at places dividing a prime , in generic situations the Serre weights of a mod modular Galois representation which is irreducible when restricted to each decomposition group above are exactly those previously predicted by Herzig. We do this by combining explicit computations in -adic Hodge theory (based on a formalism of strongly divisible modules and Breuil modules with descent data which we develop here) with a technique that we call weight cycling.
"Weight cycling and Serre-type conjectures for unitary groups." Duke Math. J. 162 (9) 1649 - 1722, 15 June 2013. https://doi.org/10.1215/00127094-2266365