The fundamental lemma and the Hitchin fibration [after Ngo Bao Chau]

摘要

This article is a Bourbaki seminar report on Ngo Bao Chau's proof of thefundamental lemma. About thirty years ago, R. P. Langlands conjectured acollection of identities to hold among integrals over conjugacy classes inreductive groups. Ngo Bao Chau has proved these identities (collectively calledthe fundamental lemma) by interpreting the integrals in terms of the cohomologyof the fibers of the Hitchin fibration. The fundamental lemma has profoundconsequences for the theory of automorphic representations. Significant recenttheorems in number theory use the fundamental lemma as an ingredient in theirproofs.