# Serre weights for U⁢(n)

• Thomas Barnet-Lamb , Toby Gee and David Geraghty

## 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.

Award Identifier / Grant number: DMS-0841491

Award Identifier / Grant number: DMS-1440703

Funding statement: The second author was partially supported by NSF grant DMS-0841491, a Marie Curie Career Integration Grant, and by an ERC Starting Grant, and the third author was partially supported by NSF grant DMS-1440703.

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