Special Year 2010-11: Galois Representations and Automorphic Forms - Seminar

I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is deduced from a potential automorphy result for...

We give a new local characterization of the Local Langlands Correspondence, using deformation spaces of p-divisible groups, and show its existence by a comparison with the cohomology of some Shimura varieties. This reproves results of Harris-Taylor...

Picard moduli spaces parametrize principally polarized abelian varieties with complex multiplication by the ring of integers in an imaginary-quadratic field. The loci where the abelian varieties split off an elliptic curve in a controlled way are...

Some automorphic forms, despite the fact they are algebraic, do not have any interpretation as cohomology classes on a Shimura variety: therefore nothing is known at present on their expected arithmetic properties. I shall explain how such forms...

Let F be a locally compact non-Archimedean field, p its residue characteristic and G a connected reductive algebraic group over F . The classical Satake isomorphism describes the Hecke algebra (over the field of complex numbers) of double classes in...