Rainer Weissauer (University of Heidelberg)
Joint Chebyshev Lab and Euler Institute Colloquium
Thursday 24 May 17:00 Euler Institute (Pesochnaya nab. 10)
Despite the tremendous progress made during the 50 years since they were formulated, the Langlands conjectures remain mysterious until today. The conjectures, in their original form, relate finite dimensional representations of the absolute Galois group of
to certain
-packets of automorphic representations
of the adele groups
, for arbitrary reductive groups
over
. This relationship should be, in a very precise way, controlled by a coincidence
of
-series, and similarly of
-factors, attached to
respectively
. Furthermore, it is supposed that the correspondence respects the local-global principle. The analogous local Langlands conjecture, linking finite dimensional representations of the absolute Galois groups for completions
of
to smooth irreducible representations of
, has been proved by Harris, Taylor and Henniart for the groups
in 2001. However, beyond this not much is known for arbitrary
. We give a survey on this, including a discussion of some recent results on the Langlands correspondence in the case
.