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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



The geometric nature of the fundamental lemma

Author: David Nadler
Journal: Bull. Amer. Math. Soc. 49 (2012), 1-50
MSC (2010): Primary 11R39, 14D24
Published electronically: July 26, 2011
MathSciNet review: 2869006
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Abstract: The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands in 1979 as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in representation theory, number theory, algebraic geometry, and algebraic topology, a proof of the Fundamental Lemma was recently completed by Ngô Bao Châu in 2008, for which he was awarded a Fields Medal. Our aim here is to touch on some of the beautiful ideas contributing to the Fundamental Lemma and its proof. We highlight the geometric nature of the problem which allows one to attack a question in $p$-adic analysis with the tools of algebraic geometry.

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Additional Information

David Nadler
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2370
MR Author ID: 620327

Received by editor(s): January 30, 2001
Received by editor(s) in revised form: April 18, 2011
Published electronically: July 26, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.