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The mod p local Langlands correspondence and supersingular representations of GL_2(F)

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

Let F be a finite extension of Q_p.  A mod p local Langlands correspondence is believed to exist between mod p representations of the absolute Galois group of F and certain mod p representations of GL_n(F).  A major obstacle to its study is that the supersingular mod p representations of GL_n(F), which are the basic building blocks of the mod p representation theory of this group, are very poorly understood.  In particular, irreducible supersingular representations of GL_2(F) have previously been constructed explicitly only when F/Q_p is unramified. We will discuss some aspects of the mod p local Langlands correspondence and the construction (in progress) of a family of irreducible supersingular representations of GL_2(F) for totally ramified F/Q_p of that form that is expected to appear in the image of the correspondence.

This talk is part of the Number Theory Seminar series.

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