Duke Mathematical Journal

Weight cycling and Serre-type conjectures for unitary groups

Abstract

We prove that for forms of $\operatorname {U}(3)$ 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

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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