Duke Mathematical Journal

Weight cycling and Serre-type conjectures for unitary groups

Matthew Emerton, Toby Gee, and 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 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.

Article information

Source
Duke Math. J., Volume 162, Number 9 (2013), 1649-1722.

Dates
First available in Project Euclid: 11 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1370955542

Digital Object Identifier
doi:10.1215/00127094-2266365

Mathematical Reviews number (MathSciNet)
MR3079258

Zentralblatt MATH identifier
1283.11083

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms

Citation

Emerton, Matthew; Gee, Toby; Herzig, Florian. Weight cycling and Serre-type conjectures for unitary groups. Duke Math. J. 162 (2013), no. 9, 1649--1722. doi:10.1215/00127094-2266365. https://projecteuclid.org/euclid.dmj/1370955542


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