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Arthur's theory of automorphic forms on classical groups (a survey)

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Non-Abelian Fundamental Groups in Arithmetic Geometry

As requested by the organizers, I will try to give the flavour of Arthur’s results describing completely the automorphic forms on orthogonal or symplectic groups. In view of the exhaustive results on Galois representations associated to forms on GL(n), I will try to explain the consequences for temperedness (or not) of cohomological representations of these groups, and possibly on the Galois representations appearing in the related Shimura varieties. This is a purely expository lecture.

This talk is part of the Isaac Newton Institute Seminar Series series.

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