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15 June 2013 Weight cycling and Serre-type conjectures for unitary groups
Matthew Emerton, Toby Gee, Florian Herzig
Duke Math. J. 162(9): 1649-1722 (15 June 2013). DOI: 10.1215/00127094-2266365

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 Herzig. 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 here) with a technique that we call weight cycling.

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Matthew Emerton. Toby Gee. Florian Herzig. "Weight cycling and Serre-type conjectures for unitary groups." Duke Math. J. 162 (9) 1649 - 1722, 15 June 2013. https://doi.org/10.1215/00127094-2266365

Information

Published: 15 June 2013
First available in Project Euclid: 11 June 2013

zbMATH: 1283.11083
MathSciNet: MR3079258
Digital Object Identifier: 10.1215/00127094-2266365

Subjects:
Primary: 11F30

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 9 • 15 June 2013
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