Skip to main content
1 of 2
Andreas Holmstrom
  • 5.6k
  • 5
  • 41
  • 62

Here are few remarks which might be relevant, although I understand almost nothing of the global Langlands program.

Lafforgue is currently working on problems relating to functoriality. There are a number of recent preprints and notes on his webpage, see for example "Quelques remarques sur le principe de fonctorialité". If you don't read French, maybe the lectures of Lafforgue in Cambridge a few months ago would be useful. They are available in various video formats at the Newton Institute webpage. To find them, see this list, and scroll down to May - there is a total of 5 talks by Lafforgue, the first one on May 5th.

My impression of Lafforgue's work is that he aims for a proof of functoriality in a fairly general setting, and (amazingly!) he hopes that the method would work also in the number field case and not only for function fields (although I might have misunderstood this). The method has at least some vague similarity with Tate's thesis, I think.

For more general background on functoriality and related things, see maybe Knapp's survey on the Langlands program, the Clay Summer School Proceedings from 2003 (here is the Google Books page), and this short note of Rapoport on Lafforgue's earlier work.

Andreas Holmstrom
  • 5.6k
  • 5
  • 41
  • 62