Serre Weights for U(n)

Abstract

We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on unitary groups of rank n for odd primes l. Given a modular Galois representation, we use automorphy lifting theorems to prove that it is modular in many other weights. We make no assumptions on the ramification or inertial degrees of l. We give an explicit strengthened result when n = 3 and l splits completely in the underlying CM field.

23 pages. arXiv admin note: substantial text overlap with arXiv:1106.5586

References in corpus (5)

• Local-global compatibility and the action of monodromy on nearby cycles
• The weight in a Serre-type conjecture for tame n-dimensional Galois representations
• On the automorphy of $l$-adic Galois representations with small residual image
• The weight part of Serre's conjecture for GL(2)
• A Note on Potential Diagonalizability of Crystalline Representations

Cited by in corpus (4)

• G-valued local deformation rings and global lifts
• Potentially crystalline deformation rings and Serre weight conjectures
• Crystalline liftings and weight part of Serre's conjecture
• Adapted bases of Kisin modules and Serre weights