Weight cycling and Serre-type conjectures for unitary groups

Abstract

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 the third author. 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 in the paper, with a technique that we call "weight cycling".

66 pages

Cited by in corpus (11)

• Ordinary representations of G(Q_p) and fundamental algebraic representations
• On mod p local-global compatibility for GL_3 in the ordinary case
• Diagrams in the mod $p$ cohomology of Shimura curves
• Weight elimination in Serre-type conjectures
• p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties
• Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor
• Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$
• Serre weight conjectures for $p$-adic unitary groups of rank 2
• On the existence of admissible supersingular representations of $p$-adic reductive groups
• Smoothness and Classicality on eigenvarieties
• Serre weights for three-dimensional wildly ramified Galois representations