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. This completes the analysis begun in [BLGG11], which proved that all predicted Serre weights occur. Our methods are purely local, using the theory of (phi,Ghat)-modules to determine the possible reductions of certain two-dimensional crystalline representations.

J. Amer. Math. Soc., to appear. Contains minor corrections from published version

References in corpus (3)

• On the automorphy of $l$-adic Galois representations with small residual image
• Serre weights for rank two unitary groups
• Crystalline representations of G_Qp^a with coefficients

Cited by in corpus (2)

• Lattices in the cohomology of Shimura curves
• A note on reductions of 2-dimensional crystalline Galois representations