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Reductions of local Galois representations arising from Hilbert modular forms

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The mod p local Langlands correspondence for GL(2,Qp) (due to Breuil, Colmez, Emerton) associates mod p representations of this group to two-dimensional representations of the absolute Galois group of Qp. I’ll discuss some of the problems arising in constructing a generalization to extensions F of Qp. In particular, I’ll explain how the representation of GL(2,F) distinguishes among non-split reducible Galois representations for unramified F. This is joint work with C. Breuil.

This talk is part of the Number Theory Seminar series.

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