The Buzzard-Diamond-Jarvis conjecture for unitary groups
Number Theory
2013-09-04 v4
Abstract
Let p > 2 be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. This completes the analysis begun in [BLGG11], which proved that all predicted Serre weights occur. Our methods are purely local, using the theory of (phi,Ghat)-modules to determine the possible reductions of certain two-dimensional crystalline representations.
Keywords
Cite
@article{arxiv.1203.2552,
title = {The Buzzard-Diamond-Jarvis conjecture for unitary groups},
author = {Toby Gee and Tong Liu and David Savitt},
journal= {arXiv preprint arXiv:1203.2552},
year = {2013}
}
Comments
J. Amer. Math. Soc., to appear. Contains minor corrections from published version