The Buzzard–Diamond–Jarvis conjecture for unitary groups

Abstract

Let p > 2 be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of (φ, Ĝ)-modules to determine the possible reductions of certain two-dimensional crystalline representations.