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
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by Toby Gee, Tong Liu and David Savitt

J. Amer. Math. Soc. 27 (2014), 389-435

DOI: https://doi.org/10.1090/S0894-0347-2013-00775-4

Published electronically: July 3, 2013

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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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