English

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

R2 v1 2026-06-21T20:32:45.182Z