The Buzzard–Diamond–Jarvis conjecture for unitary groups

Gee, Toby; Liu, Tong; Savitt, David

doi:10.1090/S0894-0347-2013-00775-4

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
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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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