The Buzzard-Diamond-Jarvis conjecture for unitary groups

Details The Buzzard-Diamond-Jarvis conjecture for unitary groups The Buzzard-Diamond-Jarvis conjecture for unitary groups

2012-03-12

arxiv.org/abs/1203.2552v1

Mathematics

Number Theory

44 pages

Scientific paper

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.

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