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arXiv · 1106.4522

Weight cycling and Serre-type conjectures for unitary groups

Matthew Emerton·Toby Gee·Florian Herzig
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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".

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Matthew Emerton, Toby Gee, Florian Herzig. 2011-06-22. Weight cycling and Serre-type conjectures for unitary groups. https://doi.org/10.1215/00127094-2266365

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