The Buzzard–Diamond–Jarvis conjecture for unitary groups
Authors:
Toby Gee, Tong Liu and David Savitt
Journal:
J. Amer. Math. Soc. 27 (2014), 389-435
MSC (2010):
Primary 11F33, 11F80
DOI:
https://doi.org/10.1090/S0894-0347-2013-00775-4
Published electronically:
July 3, 2013
MathSciNet review:
3164985
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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. Our methods are purely local, using the theory of $(\varphi ,\hat {G})$-modules to determine the possible reductions of certain two-dimensional crystalline representations.
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Additional Information
Toby Gee
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ United Kingdom
Email:
toby.gee@imperial.ac.uk
Tong Liu
Affiliation:
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907
MR Author ID:
638721
Email:
tongliu@math.purdue.edu
David Savitt
Affiliation:
Department of Mathematics, University of Arizona, 617 N. Santa Rita Avenue, Tucson, Arizona 85721-0089
Email:
savitt@math.arizona.edu
Received by editor(s):
July 5, 2012
Received by editor(s) in revised form:
May 15, 2013
Published electronically:
July 3, 2013
Additional Notes:
The second author was partially supported by NSF grant DMS-0901360.
The third author was partially supported by NSF grant DMS-0901049 and NSF CAREER grant DMS-1054032.
Article copyright:
© Copyright 2013
American Mathematical Society