Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 9 (2013), 1649-1722.
Weight cycling and Serre-type conjectures for unitary groups
We prove that for forms of which are compact at infinity and split at places dividing a prime , in generic situations the Serre weights of a mod modular Galois representation which is irreducible when restricted to each decomposition group above are exactly those previously predicted by Herzig. We do this by combining explicit computations in -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.
Duke Math. J., Volume 162, Number 9 (2013), 1649-1722.
First available in Project Euclid: 11 June 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F30: Fourier coefficients of automorphic forms
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