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The Buzzard-Diamond-Jarvis conjecture for unitary groups

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If you have a question about this talk, please contact Tom Fisher .

We will discuss the proof of the weight part of Serre’s conjecture for rank two unitary groups in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups).  This is joint work with Toby Gee and Tong Liu.  More precisely, we prove that any Serre weight which occurs is a predicted weight; this completes the analysis begun by Barnet-Lamb, Gee, and Geraghty, who proved that all predicted weights occur.  Our methods are purely local, using Liu’s theory of (phi,G-hat) modules to determine the possible reductions mod p of certain two-dimensional crystalline Galois representations.

This talk is part of the Number Theory Seminar series.

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