A re finement of the Baum-Connes conjecture for p-adic groups

Roger Plymen (University of Southampton)

Tuesday 22nd October, 2013 16:00-17:00 Maths 416


Let G be a p-adic group such as GL(n) or SL(n), and consider the Baum-Connes correspondence (due to V Laff orgue) for G. Since the LHS has never been explicitly computed for any noncommutative p-adic group, there is a case for reformulating the LHS (the "answer") in a more computable way.

Thanks to an approach of J Bernstein, we can quickly get into the world of compact tori E^s acted upon by certain fi nite groups W^s. The conjecture then says that the classical equivariant K-theory groups K_{W^s}(E^s) account for the RHS (the K-theory of the reduced C^*-algebra of G). Modulo torsion, the Chern character then supplies the answer: the cohomology of the extended
quotients E^s//W^s.

I will explain this, as far as possible from first principles, hopefully with some good examples.
(Joint work with Anne-Marie Aubert and Paul Baum)

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