Weight cycling and Serre-type conjectures for unitary groups

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 th...

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Bibliographic Details
Published in:arXiv.org 2013-06
Main Authors: Emerton, Matthew, Gee, Toby, Herzig, Florian
Format: Article
Language:English
Subjects:
Cycles
Modules
Weight
Online Access:Get full text
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Summary: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".
ISSN:2331-8422
DOI:10.48550/arxiv.1106.4522