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Colloquium: On the mod p Langlands program for GLn November 03, 2014 (04:00 PM PST - 05:00 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Christophe Breuil (Centre National de la Recherche Scientifique (CNRS))
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Let K be a finite extension of Qp. It is known for some time that one cannot expect a bijection between smooth irreducible admissible representations of GLn(K) and smooth n-dimensional representations of Gal(Kbar/K), both over Fpbar. However, one can still hope for a ``good understanding'' of the representations of GLn(K) occuring as Hecke Eigenspaces of mod p automorphic forms (for, say, compact unitary groups).

When K is unramified, I will present some conjectures on the generic structure of these GLn(K)-representations, and the way this structure is related to the underlying Gal(Kbar/K)-representation. Then I will give some fragmentary evidence (due to many people) which support these conjectures.

This is joint work (in progress) with Florian Herzig and Benjamin Schraen.

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