Weight cycling and Serre-type conjectures for unitary groups

摘要

We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representation which is irreducible when restricted to each decomposition group above p are exactly those previously predicted by Herzig. We do this by combining explicit computations in p-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.